
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
Shift the graph of the function $f(x) = \sqrt{3}\sin{2x} - \cos{2x}$ to the left by $\varphi$ units ($0 < \varphi < \frac{\pi}{2}$) to obtain the graph of the function $y = g(x)$. If $g(x) \leq |g(\frac{\pi}{6})|$ holds for all $x \in \mathbb{R}$, find the interval where $y = g(x)$ is monotonically decreasing.

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