
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 ellipse $C\_1: \frac{x^{2}}{9}+ \frac{y^{2}}{5}=1$ and the hyperbola $C\_2: x^{2}- \frac{y^{2}}{3}=1$, let $P$ be the point of intersection of $C\_1$ and $C\_2$ in the first quadrant. The distance from point $P$ to the left focus of the ellipse is $\_\_\_\_\_\_\_\_$.

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