
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 $f(x)=\frac{{(x+1)}^{2}+a\sin x}{{x}^{2}+1}+3$ ($a\in \mathbb{R}$), and $f(\ln (\log_{2}5))=5$, find the value of $f(\ln (\log_{5}2))$.

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