
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
Let  $f(x)$  be the function such that  $f(x)>0$  at  $x\geq 0$  and  $\{f(x)\}^{2006}=\int_{0}^{x}f(t) dt+1.$ 

Find the value of  $\{f(2006)\}^{2005}.$ 

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