
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
Given that the ticket price per student is $x$ dollars, a group of 45 students from 10th grade pays a total of $180$ dollars, and a group of 36 students from 11th grade pays a total of $144$ dollars, determine the number of possible values for x, where x must also be a divisor of the number of students in the 11th grade.

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