
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 hyperbola $M$: $x^{2}- \frac{y^{2}}{b^{2}}=1 (b > 0)$, its left and right foci are $F_{1}$ and $F_{2}$, respectively. A line parallel to one asymptote of the hyperbola passes through point $F_{1}$ and intersects the other asymptote at point $P$. If point $P$ lies on the parabola $y=mx^{2}$, with a focus at $(0,1)$, find the eccentricity of hyperbola $M$.

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