
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
Given the absolute magnitude of Sirius, $M_{Sirius} = 1.45$, the absolute magnitude of Betelgeuse, $M_{Betelgeuse} = -5.53$, the visual magnitude of Sirius, $m_{Sirius} = -1.45$, and the visual magnitude of Betelgeuse, $m_{Betelgeuse} = -0.73$, determine the ratio of the distances between the observer and Sirius and Betelgeuse.

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