
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
Consider the function $y=\cos\left(2x+\frac{\pi}{6}\right)$. The point $P\left(\frac{\pi}{4}, t\right)$ on its graph is shifted right by $m (m > 0)$ units to obtain the point $P'$. If $P'$ lies on the graph of the function $y=\cos 2x$, then:
A) $t=-\frac{\sqrt{3}}{2}$, and the minimum value of $m$ is $\frac{\pi}{6}$
B) $t=-\frac{\sqrt{3}}{2}$, and the minimum value of $m$ is $\frac{\pi}{12}$
C) $t=-\frac{1}{2}$, and the minimum value of $m$ is $\frac{\pi}{12}$
D) $t=-\frac{1}{2}$, and the minimum value of $m$ is $\frac{\pi}{6}$

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