
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
Callum starts with the integer $9^6$ and then alternately multiplies by 3 and divides by 2 for a total of 15 steps. The sequence starts with $9^6$, and in the next step becomes $(9^6) \times 3$, followed by $(9^6 \times 3)/2$, and so on. Determine the last number in this sequence and express it as $a^b$ where $a$ and $b$ are integers and $a$ as small as possible.

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