
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
Let  $S$  be the set of all real numbers  $x$  such that  $0 \le x \le 2016 \pi$  and  $\sin x < 3 \sin(x/3)$ .  The set  $S$  is the union of a finite number of disjoint intervals.  Compute the total length of all these intervals.

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