
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 that the function $f(x)$ defined on $\mathbb{R}$ is an odd function and satisfies $f(\frac{3}{2}-x)=f(x),f(-2)=-3,$ and 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 ${ {a_{n}} }$), find $f({a_{5}})+f({a_{6}})=$\_\_\_\_\_\_\_\_.

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