
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 functions $y=\cos x$ and $y=\sin(2x+\varphi)$ ($0 \leq \varphi \leq \pi$), their graphs intersect at a point with an abscissa of $\frac{\pi}{3}$. The value of the constant $\varphi$ is \_\_\_\_\_\_.

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