
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
For a function satisfying  $ f'(x) > 0$  for  $ a\leq x\leq b$ , let  $ F(x) \equal{} \int_a^b |f(t) \minus{} f(x)|\ dt$ . For what value of  $ x$  is  $ F(x)$  is minimized?

Present the answer in LaTex format: \boxed{Your answer}
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