
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 function $f(x) = \cos{2x}$ is translated to the left by $\phi$ ($0 < \phi < \frac{\pi}{2}$) units to obtain the function $g(x)$. If the function $g(x)$ is monotonically decreasing in the interval $[-\frac{\pi}{6}, \frac{\pi}{6}]$, and the largest negative zero of the function $g(x)$ is in the interval $(-\frac{\pi}{6}, 0)$, then the range of $\phi$ is $\_\_\_\_\_\_\_\_\_\_.$

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