
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
From the set of numbers

$$
\{2 ; 3 ; 9 ; 27 ; 81 ; 243 ; 567\}
$$

numbers $a, b, q,$ and $r$ are selected to satisfy equation (1). Find the dividend, divisor, quotient, and remainder.

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