
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 $f(x)=\left\{\begin{array}{l}(x+1)^{5},x>1\\{x}^{2}+2,x\leq 1,\end{array}\right.$, find the coefficient of $x^{4}$ in the expansion of $f\left(f\left(x\right)\right)$ when $0 < x < 1$.

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