
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 $f(x)=\sqrt{3}\sin 2x - \cos 2x$, if the graph of $f(x)$ is shifted to the left by $\frac{\pi}{6}$ units to obtain the graph of $g(x)$, then the graph of $g(x)$ can be obtained by shifting the graph of $y=2\cos 2x$ to the right by at least ______ units.

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