
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 shifted 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 $|f(x_1) - g(x_2)| = 4$, we have $|x_1 - x_2|_{\min} = \frac{\pi}{6}$, then $\varphi = \_\_\_\_\_\_$.

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