
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
The graph of the function $f(x)=2\sin 2x$ is translated to the left by $\frac{\pi}{6}$ units and then upward by $1$ unit to obtain the graph of the function $y=g(x)$. Find all possible values for the number of zeros of $y=g(x)$ in the interval $[a,a+10\pi]$ for any $a \in \mathbb{R}$.

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