
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 \( a \geqslant 0 \), for any \( m \) and \( x \) (\( 0 \leqslant m \leqslant a, 0 \leqslant x \leqslant \pi \)), it holds that
$$
|\sin x - \sin (x + m)| \leqslant 1.
$$
Find the maximum value of \( a \).

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