
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
In which bases is it true that the rule for divisibility by four is like the rule for divisibility by nine in the decimal system, and the rule for divisibility by nine is like the rule for divisibility by four in the decimal system?

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