
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 operation $\oplus$ is defined as $a\oplus b=a$ when $a\geqslant b$ and $a\oplus b=b^{2}$ when $a \lt b$, and the function $f(x) = (1\oplus x)\cdot x + (2\oplus x)$, determine the maximum value of $f(x)$ for $x\in [-2,2]$.

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