
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
For any closed interval \( I \), let \( M_{1} \) represent the maximum value of the function \( y=\sin x \) on \( I \). If the positive number \( a \) satisfies \( M_{[0, a]}=2 M_{[a, 2 a]} \), then the value of \( a \) is \(\quad\) .

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