
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 $y=\cos (2x+\frac{\pi }{6})$, a point $P(\frac{\pi }{4},t)$ on its graph is moved right by $m (m>0)$ units to a new point $P'$, where $P'$ lies on the graph of the function $y=\cos 2x$. Determine the value of $t$ and the minimum value of $m$.

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