
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
Consider a parabola described by the equation $y^2 = x$. A line $l$ that passes through the focus $F$ of the parabola intersects the parabola at points $A$ and $B$, where the angle of inclination $\theta$ of line $l$ satisfies $\theta \geqslant \frac{\pi}{4}$. If point $A$ lies above the x-axis, find the range of values for $|FA|$.

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