
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
Explore the task based on the following information:

如何设计招聘方案? (How to design a recruitment plan?)

| Information | Description |
|-------------|-------------|
| Material 1  | A certain car manufacturer is developing a new electric car and plans to produce and install 240 cars in a year. Each skilled worker can independently install an electric car. Due to the inability to allocate enough skilled workers to complete the installation of the new electric cars, the factory decides to recruit some new workers who can be trained to work independently. |
| Material 2  | The research department found that 2 skilled workers and 3 new workers can install 14 electric cars per month; 3 skilled workers and 2 new workers can install 16 electric cars per month. |
| Material 3  | The factory pays a monthly salary of $2000 to each skilled worker who installs electric cars and $1200 to each new worker. |

| Task | Description |
|------|-------------|
| Task 1 | Analyze the quantity relationship: How many electric cars can each skilled worker and new worker install per month? |
| Task 2 | Determine a feasible plan: If the factory recruits $n$ new workers ($0 < n < 5$) so that the recruited new workers and the allocated skilled workers can just complete the installation task for a year, what are the possible recruitment plans for the factory? |
| Task 3 | Select the optimal plan: In the above plan, to save costs, how many new workers should be recruited? (Write down the answer directly) |

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