
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 disc is divided into  $12$  equal sectors and one of  $6$  different colours is used to colour each sector. No two adjacent sectors can have the same colour. Find the number of such distinct colorings possible.

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