
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 a function such that  $ 1\minus{}f(x)\equal{}f(1\minus{}x)$  for  $ 0\leq x\leq 1$ .

Evaluate  $ \int_0^1 f(x)\ dx$ .

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