
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 parabola $C\_1$: $y=-\frac{1}{2p}x^2 (p > 0)$ and the hyperbola $C\_2$: $\frac{x^2}{3} - y^2 = 1$, the line connecting the focus of the parabola and the left focus of the hyperbola intersects $C\_1$ at point $M$ in the third quadrant. If the tangent of $C\_1$ at point $M$ is parallel to one of the asymptotes of $C\_2$, find the value of $P$.

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