
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
Starting with $10^6$, Sally creates a sequence by first multiplying by 3, then dividing by 2, and repeats these steps. Write the last integer of this 12-step sequence in the form $a^b$, where $a$ and $b$ are positive integers and $a$ is as small as possible.

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