
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 $f(x) = x^2 + 2x$ ($x > 0$), $f_1(x) = f(x)$, $f_{n+1}(x) = f(f_n(x))$, where $n \in \mathbb{N}^*$, calculate the maximum value of $f_5(x)$ on the interval $[1, 2]$.

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