
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
Consider the sequence starting with the number 8820, created by first repeatedly dividing by 2 until no longer divisible by 2, and then subsequently dividing by 5 as long as divisibility by 5 continues. How many integer terms are in this sequence?

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