
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 $f(x)=2\cos 2x$ is translated to the right by $\varphi$ $(0 < \varphi < \frac{\pi}{2})$ units to obtain the graph of the function $g(x)$. If for $x_{1}$ and $x_{2}$ that satisfy $|f(x_{1})-g(x_{2})|=4$, the minimum value of $|x_{1}-x_{2}|$ is $\frac{\pi}{6}$, then $\varphi=$____.

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