
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 $a \otimes b = \begin{cases} a, & \text{if } a \leqslant b \\ b, & \text{if } a > b \end{cases}$ and the function $f(x) = \sin x \otimes \cos x \, (x \in \mathbb{R})$, find the maximum value of the function $f(x)$.

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