
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 curve \( C_{1}: x^{2}+y^{2}=1 \) and the curve \( C_{2}: x+y=1 \). Point \( P \) is on \( C_{2} \). The ray \( OP \) intersects \( C_{1} \) at \( R \). Another point \( Q \) is on \( OP \) and satisfies \( |O Q| \cdot |O P| = |O R|^{2} \). Find the equation of the trajectory of point \( Q \) as \( P \) moves along the curve \( C_{2} \).

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