
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 a regular $n$-gon ($n \geqslant 5$) with center $O$, two adjacent vertices of the $n$-gon are denoted by $A$ and $B$. Consider a triangle $\triangle XYZ$ that is congruent to $\triangle OAB$. Initially, $\triangle XYZ$ overlaps with $\triangle OAB$. Subsequently, $\triangle XYZ$ is moved in the plane such that points $Y$ and $Z$ move along the perimeter of the $n$-gon while point $X$ moves inside the $n$-gon. Find the trajectory of point $X$.

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