
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 $F(0,1)$, and the line $l:y=-1$, if a moving point $M$ has equal distances to point $F$ and to the line $l$.

  

$(1)$ Find the equation of the trajectory $E$ of the moving point $M$;

$(2)$ The line $l$ passes through point $F$ and intersects the curve $E$ at two distinct points $A$, $B$. If the slope angle of line $l$ is $\alpha = 60^\circ$, find the length of chord $AB$.

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