
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 $10^7$, Caroline alternates between dividing by 5 and multiplying by 3. She does this a total of 14 steps, beginning with division by 5. What is the last integer in her sequence? Express your answer 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}
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