
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 \(10^7\), Carol alternates operations by dividing by 3 in the first step and then multiplying by 2 in the next step. This creates a sequence of numbers starting from \(10^7\). What is the last integer in her sequence after 14 steps? 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}
user