
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
Translate the following function $f(x)=\cos(2x+\varphi)$ where $|\varphi| < \dfrac{\pi}{2}$, so that its graph is shifted to the left by $\dfrac{\pi}{6}$ units. If the resulting graph is symmetric about the $y$-axis, the minimum value of $f(x)$ in the interval $\left[\dfrac{\pi}{12}, \dfrac{\pi}{2}\right]$ is ___.
A) $- \dfrac{\sqrt{3}}{2}$
B) $- \dfrac{1}{2}$
C) $\dfrac{1}{2}$
D) $\dfrac{\sqrt{3}}{2}$

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