
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 $f(x)$ with domain $R$, $f(x+1)$ is even, $f(x+2)$ is odd, and $f(x) = ax^2 + b$ for $x \in [1,2]$. If $f(0)+f(3)=6$, find the value of $f(5)$.

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