
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
Yuan Da Trading Co., Ltd. currently has 100 salespersons, with an average annual performance income of $a$ yuan per person. To adapt to the needs of market development, a branch office is opened in a certain city, and some elite salespersons are needed to explore the market. The company found that after personnel adjustment, the performance income of the salespersons remaining at the headquarters could increase by 20%, while the average annual performance income of the salespersons sent to the branch could reach $3.5a$ yuan per person. To maintain the long-term interests of the company, it is necessary to ensure that after the personnel adjustment, the total annual income of the headquarters is not less than before the adjustment, and the total income of the branch is not less than half of the total annual income of the company before the adjustment. Please help the company's leaders decide how many elite salespersons need to be sent to the branch.

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