
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 graph of the function $y=\cos (2x+\varphi )(-\pi \leqslant \varphi \leqslant \pi )$ is translated to the right by $\dfrac{\pi }{2}$ units, and then coincides with the graph of the function $y=\sin (2x+\dfrac{\pi }{3})$. Find the value of $\varphi$.

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