
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
During the summer vacation, two parents plan to take several students on a tour. They contacted two travel agencies with a quoted price of $\\(500\\)$ yuan per person. After negotiation, Travel Agency A offers a discount where both parents pay the full price, and students pay $70%$ of the price; Travel Agency B offers an $80%$ discount for both parents and students. Assuming these two parents take $x$ students on the tour, which travel agency should they choose?

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