
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 the parabola $E$:${y}^{2}=4x$, its focus $F$, and its directrix $l$. $l$ intersects the $x$-axis at point $T$, $A$ is a point on $E$, $AA_{1}$ is perpendicular to $l$ with foot $A_{1}$, $A_{1}F$ intersects the $y$-axis at point $S$. If $ST$ is parallel to $AF$, then $|AF|=$ \_\_\_\_\_\_\_\_\_.

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