
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
 $21$  Savage has a  $12$  car garage, with a row of spaces numbered  $1,2,3,\ldots,12$ . How many ways can he choose  $6$  of them to park his  $6$  identical cars in, if no  $3$  spaces with consecutive numbers may be all occupied?

*2018 CCA Math Bonanza Team Round #9*

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