
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
The principal of a school plans to lead the city-level "Outstanding Students" to Beijing for a trip during the summer vacation. Travel Agency A says, "If the principal buys a full-price ticket, the rest of the students can enjoy a half-price discount." Travel Agency B says, "Including the principal, everyone will enjoy a 40% discount off the full ticket price (i.e., charged at 60% of the full ticket price)." If the full ticket price is 240 yuan.  
(Ⅰ) Let the number of students be $x$, the charge by Travel Agency A be $y_{\text{甲}}$, and the charge by Travel Agency B be $y_{\text{乙}}$, calculate the charges by the two travel agencies respectively (establish the expressions);  
(Ⅱ) When the number of students is what, the charges by the two travel agencies are the same;  
(Ⅲ) Discuss which travel agency is more cost-effective based on the number of students $x$.

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