
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
The hyperbola $\frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1\left(a \gt 0,b \gt 0\right)$ has an asymptote passing through the point $P(-1,\sqrt{3})$. $F_{1}$ and $F_{2}$ are the left and right foci of the hyperbola, respectively, and $|PF_{1}|=2$. If a point $M$ on the hyperbola satisfies $|MF_{1}|=\frac{5}{2}$, calculate $|MF_{2}|$.

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