
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 that the state income tax is levied at the rate of $(p-1)\%$ of the first $\textdollar 30000$ of annual income, $(p+1)\%$ of the next $\textdollar 20000$, and $(p+3)\%$ of any amount above $\textdollar 50000$, and the total tax paid is $(p+0.5)\%$ of the annual income, determine Linda's annual income.

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