
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
We want to draw a digit on each face of two identical cubes such that, by suitably rotating them and placing them next to each other, we can display the date of any day of the month. For coherence, single-digit days are also displayed with two digits, where the first is a leading zero. How many ways are there to choose the digits to be drawn on each of the cubes? (The order of the six digits chosen for each cube does not matter in the count.)

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