
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 \( f(z) = \int_0^z \sqrt{x^4 + (z - z^2)^2} \, dx \). Find the maximum value of \( f(z) \) in the range \( 0 \leq z \leq 1 \).

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