
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 the curve $C$: $\begin{cases} & x=2\cos \varphi, \\ & y=\sqrt{3}\sin \varphi. \end{cases}$ ($\varphi$ is a parameter) and its intersection points with the $x$-axis are $M$ and $N$, find the product of the slopes of the lines $PM$ and $PN$, where $P$ is a moving point on the curve $C$ and is not on the coordinate axes.

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