
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 equation $m_{2}-m_{1}=\frac{5}{2}\lg \frac{{E}_{1}}{{E}_{2}}$, where the magnitude of a star with magnitude $m_{k}$ is $E_{k}(k=1,2)$, determine the ratio of the brightness of the Sun to Sirius.

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