code: def identify_frontdoor(
      graph: nx.DiGraph,
      action_nodes: List[str],
      outcome_nodes: List[str],
      observed_nodes: List[str],
      dseparation_algo: str = "default",
  ):
      """Find a valid frontdoor variable set if it exists."""
      frontdoor_var = None
      frontdoor_paths = None
      fdoor_graph = None
      if dseparation_algo == "default":
          cond1_graph = do_surgery(
              graph, action_nodes, remove_incoming_edges=True
          )
      elif dseparation_algo == "naive":
          frontdoor_paths = get_all_directed_paths(
              graph, action_nodes, outcome_nodes
          )
      else:
          raise ValueError(
              f"d-separation algorithm {dseparation_algo} is not supported"
          )
  
      eligible_variables = (
          get_descendants(graph, action_nodes)
          - set(outcome_nodes)
          - set(get_descendants(graph, outcome_nodes))
      )
      eligible_variables = eligible_variables.intersection(
          set(observed_nodes)
      )
      set_sizes = range(1, len(eligible_variables) + 1, 1)
      for size_candidate_set in set_sizes:
          for candidate_set in itertools.combinations(
              eligible_variables, size_candidate_set
          ):
              candidate_set = list(candidate_set)
              # Cond 1: All directed paths intercepted by candidate_var
              cond1 = check_valid_frontdoor_set(
                  graph,
                  action_nodes,
                  outcome_nodes,
                  candidate_set,
                  frontdoor_paths=frontdoor_paths,
                  new_graph=cond1_graph,
                  dseparation_algo=dseparation_algo,
              )
              logger.debug(
                  "Candidate frontdoor set: {0}, Cond1: is_dseparated: {1}".format(
                      candidate_set, cond1
                  )
              )
              if not cond1:
                  continue
              # Cond 2: No confounding between treatment and candidate var
              cond2 = check_valid_backdoor_set(
                  graph,
                  action_nodes,
                  candidate_set,
                  set(),
                  backdoor_paths=None,
                  dseparation_algo=dseparation_algo,
              )["is_dseparated"]
              if not cond2:
                  continue
              # Cond 3: treatment blocks all confounding between candidate_var and outcome
              bdoor_graph2 = do_surgery(
                  graph, candidate_set, remove_outgoing_edges=True
              )
              cond3 = check_valid_backdoor_set(
                  graph,
                  candidate_set,
                  outcome_nodes,
                  action_nodes,
                  backdoor_paths=None,
                  new_graph=bdoor_graph2,
                  dseparation_algo=dseparation_algo,
              )["is_dseparated"]
              is_valid_frontdoor = cond1 and cond2 and cond3
              if is_valid_frontdoor:
                  frontdoor_var = candidate_set
                  break
      return parse_state(frontdoor_var)
  
imports: import itertools
  import logging
  from enum import Enum
  from typing import Dict, List, Optional, Union
  import networkx
  import sympy
  import sympy.stats
  from dowhy.causal_identifier.efficient_backdoor import EfficientBackdoor
  from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand
  from dowhy.graph import check_dseparation, check_valid_backdoor_set, check_valid_frontdoor_set, check_valid_mediation_set, do_surgery, get_all_directed_paths, get_backdoor_paths, get_descendants, get_instruments, has_directed_path
  from dowhy.utils.api import parse_state
label_desc: Use image node_id 11 for calling a global function with example usage: identify_frontdoor(graph, action_nodes, outcome_nodes, observed_nodes, dseparation_algo) and returns: parse_state