
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
In how many distinct ways can I arrange my seven keys on a keychain, if I want to place my house key, car key, and office key next to each other in any order? Two arrangements are not considered different if the keys can be made to be in the same order by reflection or rotation.

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