
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 that point $A(x_{0},y_{0})(x_{0}{\neq }0)$ is the intersection point of one asymptote of the parabola $C_{1}$: $y^{2}{=}2px(p{ > }0)$ and the hyperbola $C_{2}$: ${\dfrac{x^{2}}{a^{2}}{-}}{\dfrac{y^{2}}{b^{2}}}{=}1(a{ > }0{,}b{ > }0)$, if the distance from point $A$ to the axis of symmetry of the parabola $C_{1}$ is $p^{2}$, and the eccentricity of the hyperbola is equal to ${\sqrt{5}}$, find the value of $p$.

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