
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
(1) Find the equation of the parabola with the vertex at the origin, the coordinate axes as the axes of symmetry, and passing through the point $P(-2,-4)$.
(2) Let the focus of the parabola $y^{2}=2px (p > 0)$ be $F$, and point $A(0,2)$. If the midpoint $B$ of line segment $FA$ is on the parabola, what is the distance from $B$ to the directrix of this parabola?

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