
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 a number ten million, James creates a sequence of operations where he alternately divides the number by 2 for three times and then multiplies it by 5 once. This sequence goes: \(10^7\), then divide, divide, divide, and multiply, and repeats this process until a total of 12 operations have been completed. What is the last integer in this 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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