
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 $C$: $\frac{x^{2}}{4}+ \frac{y^{2}}{3}=1$, its left focus $F$ forms a line $l$ with an inclination angle of $60^{\circ}$ intersecting the ellipse $C$ at points $A$ and $B$. Find the value of $\frac{1}{|AF|}+ \frac{1}{|BF|}$.

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