
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
A function $y=f(x)$ is defined on the set of real numbers $R$ and is odd. It satisfies the condition $f(x)=f(1-x)$ for any $t\in R$, and $f(x)=2x^2$ when $x\in (0, \frac{1}{2}]$. Determine the value of $f(3)+f(-\frac{5}{2})$.

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