
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
12 Smurfs are sitting around a round table. Each Smurf dislikes the 2 Smurfs adjacent to them but does not dislike the remaining 9 Smurfs. Papa Smurf wants to send out a team of 5 Smurfs to rescue Smurfette, who was captured by Gargamel. The team should be composed such that no two members dislike each other. In how many ways can such a team be formed?

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