
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
In a city, a new taxation system has been introduced: A baseline tax of 5% is applied on the first $5,000 of income, and for any income exceeding $5,000, an additional tax rate of $(x-5)\%$ applies to the excess, where x is the total income in thousand dollars. What income, in dollars, will yield the greatest take-home pay?

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