
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
At a certain school, concert tickets are sold at a price of \( x \) dollars each, where \( x \) is a positive integer. A group of 7th graders buys tickets costing a total of \( \$60 \), another group of 8th graders buys tickets costing a total of \( \$84 \), and a group of 9th graders buys tickets costing a total of \( \$126 \). How many possible values are there for \( x \)?
A) 3
B) 4
C) 5
D) 6
E) 7

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