Ben is climbing a tree with a lot of branches. His height off the ground at time $t$ is $2t^2-5t+29$ feet. To the nearest foot, what will his minimum height be?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Ben is climbing a tree with a lot of branches. His height off the ground at time $t$ is $2t^2-5t+29$ feet. To the nearest foot, what will his minimum height be?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
26
Ben is climbing a tree with a lot of branches. His height off the ground at time $t$ is $2t^2-5t+29$ feet. To the nearest foot, what will his minimum height be?
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