
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
Two circles are centered at the origin. The point \( P(8,6) \) is on the larger circle and the point \( S(0, k) \) is on the smaller circle. If the distance \( QR = 3 \), calculate the value of \( k \).

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