
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 a function $f(x)$ defined on $\mathbb{R}$ that is an odd function and satisfies $f(3-x)=f(x)$, with $f(-1)=3$, and the sequence $\{a_n\}$ satisfies $a_1=1$ and $a_n=n(a_{n+1}-a_n)$ $(n\in \mathbb{N}^*)$, calculate $f(a_{36})+f(a_{37})$.

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