
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
In the Cartesian coordinate system $(xOy)$, the asymptotes of the hyperbola $({C}_{1}: \frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1 (a > 0,b > 0) )$ intersect with the parabola $({C}_{2}:{x}^{2}=2py (p > 0) )$ at points $O, A, B$. If the orthocenter of $\triangle OAB$ is the focus of $({C}_{2})$, find the eccentricity of $({C}_{1})$.

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