
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
Given the function \(f(x) = \begin{cases}
-x^2 + 2x, & x \leq 2, \\
\log_2 x - 1, & x > 2,
\end{cases}\), find the value of \(f(f(4))\) and the interval of \(x\) where \(f(x)\) is monotonically decreasing.

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