
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 that a math olympiad started at 9:00 and ended at 13:00, at which point the clock's hands had fallen off the axis but remained in the position they were when the clock was functioning correctly, determine the exact time the clock stopped. The hour and minute hands are superimposed exactly, forming an angle (not zero) less than $120^{\circ}$ with the second hand. Provide the exact stopping time in hours, minutes, and seconds, with a maximum error of one second. Assume the clock hands advanced continuously when it was functioning.

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