
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
Through the fixed point \( F(2,0) \), draw a line \( l \) intersecting the \( y \)-axis at point \( Q \). From point \( Q \), draw \( Q T \perp F Q \) intersecting the \( x \)-axis at point \( T \). Extend \( T Q \) to point \( P \), such that \( |T Q| = |Q P| \). Find the equation of the locus of point \( P \).

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