
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
Claude Shannon, known as the father of information theory, proposed a famous formula: $C=W\log _{2}(1+\frac{S}{N})$. In the formula, $C$ represents the limit value of data rate in units of $bit/s$; $W$ represents the channel bandwidth in units of $Hz$; $\frac{S}{N}$ represents the signal-to-noise ratio. The Shannon formula plays an important role in 5G technology. From the Shannon formula, it can be seen that to increase the transmission speed of information, it is crucial to increase the bandwidth ($W$) and the signal-to-noise ratio ($\frac{S}{N}$). If the channel bandwidth is increased from $200Hz$ to $1000Hz$, and at the same time the signal-to-noise ratio $\frac{S}{N}$ is increased from $255$ to $1023$, then the maximum data transmission speed becomes ____ times the original speed.

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