
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
To measure the brightness of stars, the ancient Greek astronomer Hipparchus first proposed the concept of stellar magnitude in the second century BC. The smaller the value of stellar magnitude, the brighter the star; the larger the value of stellar magnitude, the dimmer the star. By the year 1850, due to the application of photometers in the measurement of celestial luminosity, the British astronomer Pogson introduced the concept of brightness. The brightness of celestial bodies can be described using either stellar magnitude or brightness. The stellar magnitudes and brightness of two stars satisfy the equation $m_{1}-m_{2}=2.5(\lg E_{2}-\lg E_{1})$, where the brightness of a star with stellar magnitude $m_{k}$ is $E_{k}$ $(k=1,2)$. Given that the stellar magnitude of "Sirius" is $1.00$ and the stellar magnitude of "Altair" is $1.25$, the brightness of "Sirius" is approximately ____ times that of "Altair". (Round the result to $0.01$. When $|x|$ is small, $10^{x}\approx 1+2.3x+2.7x^{2}$)

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