
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
Define a new operation $\circledast$: when $a \geqslant b$, $a \circledast b = a$; when $a < b$, $a \circledast b = b^2$. Find the maximum value of the function $f(x) = (1 \circledast x)x - (2 \circledast x)$ over the interval $x \in [-2, 2]$.

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