
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 hyperbola $C:\frac{{{x^2}}}{{{a^2}}}-\frac{{{y^2}}}{{27}}=1({a＞0})$ with left and right foci $F_{1}$ and $F_{2}$ respectively, and one of its asymptotes has a slope of $\frac{π}{3}$. If point $P$ lies on the hyperbola and $|PF_{1}|=7$, then $|PF_{2}|=$____.

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