
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 curve $y=A\sin(2\omega x)+k$ ($A>0$, $k>0$) intersects the lines $y=4$ and $y=-2$ within the interval $\left[0, \frac{\pi}{\omega}\right]$ and the lengths of the chords cut by these lines are equal and non-zero. Then, the parameters $A$ and $k$ must simultaneously satisfy \_\_\_\_\_\_.

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