
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 $f(x)=\cos (2x+\varphi)$, where $|\varphi| \leqslant \frac{\pi}{2}$, if $f\left( \frac{8\pi}{3}-x\right)=-f(x)$, determine the horizontal shift required to obtain the graph of $y=\sin 2x$.

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