
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
Consider the hyperbola $C$: $\frac{x^{2}}{a^{2}}-y^{2}=1 (a > 0)$ and the line $l$: $x+y=1$. The hyperbola $C$ intersects the line $l$ at two points $A$ and $B$. Determine the range of values for the eccentricity $e$ of the hyperbola $C$.

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