
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 centered at the origin are given. The point $P(5,12)$ is on the larger circle, and the point $S(0,k)$ is on the smaller circle. If $QR=5$ and $\angle QOR = 30^\circ$, determine the value of $k$.

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