
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 function $f(x) = 2\sin \left( \frac{\pi}{3}x+ \frac{\pi}{6}\right)+2$, for any $a\in[1,2)$, find the range of $m$ such that the equation $f(x)-a=2$ has two distinct real roots, $0\leqslant x < m$.

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