
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 perpendicular line is drawn from the right focus \(F\) of a hyperbola to the line containing the real axis, intersecting the hyperbola at points \(A\) and \(B\). Let the left vertex of the hyperbola be \(M\). If point \(M\) is inside the circle with \(AB\) as its diameter, then the range of the eccentricity \(e\) of this hyperbola is.

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