
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
A line passing through the left focus $F_1$ of the hyperbola $\frac{x^2}{4}-\frac{y^2}{3}=1$ intersects the left branch of the hyperbola at points $M$ and $N$, with $F_2$ being its right focus. Find the value of $|MF_2| + |NF_2| - |MN|$.

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