
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
Given that Sophia is currently 3 times as old as her daughter Bella and her husband Nathan is 4 years older than Sophia, and Bella will turn 5 years old today, determine the number of Bella's future birthdays, excluding today, when Nathan's age will be an integral multiple of Bella's age when Bella turns 21 years old.

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