
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
Alison is eating 2401 grains of rice for lunch. She eats the rice in a very peculiar manner: every step, if she has only one grain of rice remaining, she eats it. Otherwise, she finds the smallest positive integer \( d > 1 \) for which she can group the rice into equal groups of size \( d \) with none left over. She then groups the rice into groups of size \( d \), eats one grain from each group, and puts the rice back into a single pile. How many steps does it take her to finish all her rice?

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