
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 an ellipse $x^{2}+\frac{{y}^{2}}{{b}^{2}}=1\left(0 \lt b \lt 1\right)$ with left and right foci $F_{1}$ and $F_{2}$, with $O$ as the vertex, and $F_{2}$ as the focus. Let the parabola intersect the ellipse at point $P$, where $\angle PF_{1}F_{2}=45^{\circ}$. Find the equation of the directrix of the parabola.

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