
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 equation of a curve in polar coordinates is given by $r = p \sin 5 \vartheta$ (where $p$ is a given length, $r$ is the radius vector corresponding to certain points of the curve, and $\vartheta$ is the corresponding angle). Construct the curve and express its equation in Cartesian coordinates.

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