
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
A certain middle school organized an art evening to enrich the students' extracurricular activities, preparing to purchase a certain number of notebooks and neutral pens (with the same price for each notebook and each neutral pen) as prizes. If purchasing $4$ notebooks and $3$ neutral pens costs a total of $38$ yuan, and purchasing $1$ notebook and $6$ neutral pens costs a total of $20$ yuan.<br/>$(1)$ How much does it cost to purchase one notebook and one neutral pen each?<br/>$(2)$ The school plans to purchase a total of $60$ notebooks and neutral pens as prizes, and according to the regulations, the total cost of the purchase does not exceed $330$ yuan. What is the minimum number of neutral pens the school must purchase?

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