
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 parliament consists of 30 members. Each pair of members are either friends or enemies, and each member has exactly 6 enemies. Every set of 3 members forms a 3-member committee. A committee is called a "good committee" if all three members are either mutual friends or mutual enemies. Determine the number of all good committees.

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