
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
Patricia wants to write digits on the faces of two wooden cubes such that any day of the month can be represented by combining a digit from one cube's face and a digit from the other cube's face. For example, to represent the first day of the month, Patricia can combine the cubes to show the faces:

For the 26th day of the month, Patricia positions the cubes to show the faces:

\[ 2\ 6 \]

The digit 6 can be used to represent 9 by rotating the face. Additionally, remember that the days of a month range from 01 to 31.

a) Which digits should be written on both cubes?

b) Find which digits should be written on each cube.

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