
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 that the even function $y=2\sin (ωx+φ)(ω > 0,0 < φ < π)$ intersects with the line $y=2$ at two points with x-coordinates $x_1$ and $x_2$, and the minimum value of $|x_2-x_1|$ is $π$, determine the interval where the function is monotonically increasing.

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