
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 a parabola with its axis of symmetry being the coordinate axis, its vertex at the origin, and the equation of the directrix being $x=-1$. A line $l$ intersects the parabola at two distinct points $A$ and $B$.
1. Find the standard equation of the parabola.
2. If the line $l$ passes through the focus of the parabola, find the value of $\overrightarrow {OA}\cdot \overrightarrow {OB}$.
3. If $\overrightarrow {OA}\cdot \overrightarrow {OB}=-4$, does the line $l$ necessarily pass through a fixed point? If it does, find the fixed point; if not, explain why.

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