
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 that the focus of the parabola $y^2 = 2px$ ($p > 0$) and the right focus $F_2$ of the hyperbola $x^{2}- \frac {y^{2}}{3}=1$ coincide, find the standard equation of the parabola. Let $P$ be a common point of the parabola and the hyperbola, find the distance from $P$ to the left focus $F_1$ of the hyperbola.

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