
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
A circular arrangement consists of 12 seats numbered consecutively from 1 to 12. A student begins shading from seat 1, then skips one seat and shades seat 3, skips two seats and shades seat 6, skips three seats and shades seat 10, and continues in this manner. Determine the number of the shaded seat that first ensures each of the 12 seats has been shaded at least once.

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