
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 \( C: y^{2} = 4x \), its focus is \( F \). The intersection of the axis of symmetry and the directrix is \( T \). Let \( P \) be any point on the parabola \( C \). When \(\frac{|PF|}{|PT|}\) attains its minimum value, find the measure of angle \(\angle PTF\).

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