
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
Dima's mother told him he needed to eat 13 spoons of porridge. Dima told his friend that he ate 26 spoons of porridge. Each subsequent child, when talking about Dima's feat, increased the number of spoons by 2 or 3 times. Eventually, one of the children told Dima's mother that Dima ate 33,696 spoons of porridge. How many times in total, including Dima, did the children talk about Dima's feat?

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