
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 equation of an ellipse as \\( \frac{x^{2}}{4}+y^{2}=1\\), its left and right foci are denoted by \\(F\_1\\) and \\(F\_2\\), respectively. A line passing through the left focus with a slope of \\(1\\) intersects the ellipse at points \\(A\\) and \\(B\\). Determine the value of \\( \frac{1}{|F\_1A|} + \frac{1}{|F\_1B|}=\_\_\_\_\_\_\ \cdot\\)

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