
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 Shannon formula $C=W\log_2(1+\frac{S}{N})$ and the signal-to-noise ratio $\frac{S}{N}$, calculate the approximate percentage increase in $C$ when the bandwidth $W$ increases by $20\%$ and $\frac{S}{N}$ increases from $1000$ to $4000$.

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