
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
Abbot writes the letter \( A \) on the board. Every minute, he replaces every occurrence of \( A \) with \( AB \) and every occurrence of \( B \) with \( BA \), hence creating a string that is twice as long. After 10 minutes, there are \( 2^{10} = 1024 \) letters on the board. How many adjacent pairs are the same letter?

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