
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
 Determine all sequences of equal ratios of the form 

     \[
     \frac{a_1}{a_2} = \frac{a_3}{a_4} = \frac{a_5}{a_6} = \frac{a_7}{a_8}
     \]

     which  simultaneously satisfy the following conditions:

      $\bullet$  The set  $\{ a_1, a_2, \ldots , a_8 \}$  represents all positive divisors of  $24$ .

      $\bullet$   The common value of the ratios is a natural number.

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