
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
Alex is trying to open a lock whose code is a sequence that is three letters long, with each of the letters being one of  $\text A$ ,  $\text B$  or  $\text C$ , possibly repeated. The lock has three buttons, labeled  $\text A$ ,  $\text B$  and  $\text C$ . When the most recent  $3$  button-presses form the code, the lock opens. What is the minimum number of total button presses Alex needs to guarantee opening the lock?

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