
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 six keys on a keychain, if my house key must be exactly opposite my car key and my office key should be adjacent to my house key? For arrangement purposes, two placements are identical if one can be obtained from the other through rotation or flipping the keychain.

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