
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 the eighth grade, students organized a trip during the summer vacation, with 10 parent representatives joining the group. Travel agency A said: "If all 10 parent representatives buy full-price tickets, the rest of the students can enjoy a half-price discount"; Travel agency B said: "Including the 10 parent representatives, everyone will receive a 40% discount off the ticket price," with the full ticket price being $40. Please calculate and explain: for what range of the number of travelers would choosing travel agency A result in lower costs?

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