
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 $f(x) = \frac{\sqrt{3}}{2}\sin 2x + \frac{1}{2}\cos 2x$, if its graph can be obtained from shifting the graph of $y = \sin 2x$ to the left by $\varphi$ units, determine the minimum value of $\varphi$.

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