
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
Which digits can be placed in the letters $A, B, C$ to make the following multiplication correct: $\overline{A B B C} \cdot \overline{C C A} = \overline{C C C C A C}$? - In which other base number systems can the problem still be solved?

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