If $P(x) = 4+2\sqrt{x+2}$ and $G(x) = 4-3x$, then what is the largest constant $a$ such that $P(G(a))$ is defined?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $P(x) = 4+2\sqrt{x+2}$ and $G(x) = 4-3x$, then what is the largest constant $a$ such that $P(G(a))$ is defined?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
2
If $P(x) = 4+2\sqrt{x+2}$ and $G(x) = 4-3x$, then what is the largest constant $a$ such that $P(G(a))$ is defined?
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