
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

Anna writes integers one below the other. Starting from a given number, she writes in the next row either the sum of the digits or the product of the digits of the previous number. She observed that every number written is odd. How many starting values of at most six digits exist such that every number written is odd?

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