
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 $\mathbb{R}$, which is an odd function and satisfies $f\left( \frac{3}{2}-x\right)=f(x)$, and $f(-2)=-3$. The sequence $\{a_n\}$ satisfies $a_1=-1$, and $\frac{S_n}{n}=2\times \frac{a_n}{n}+1$, (where $S_n$ is the sum of the first $n$ terms of $\{a_n\}$). Calculate $f(a_5)+f(a_6)$.

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