
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
A store sells shirts, water bottles, and chocolate bars. Shirts cost $10 each, water bottles cost $5 each, and chocolate bars cost $1 each. On one particular day, the store sold \( x \) shirts, \( y \) water bottles, and \( z \) chocolate bars. The total revenue from these sales was $120. If \( x, y \) and \( z \) are integers with \( x>0, y>0 \) and \( z>0 \), how many possibilities are there for the ordered triple \( (x, y, z) \)?

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