
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 $f(x)=|\sin^2 x - \sqrt{3}\cos x \cos\left(\frac{3\pi}{2} - x\right) - \frac{1}{2}|$, if the graph of the function $y=f(x)$ is translated $a$ units to the left $(0 < a < \pi)$ and the resulting graph is symmetric about the $y$-axis, then the set of all possible values for the real number $a$ is ______.

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