
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
Two sides of a triangle measure 7 cm and 10 cm. If the perimeter of the triangle is not more than 30 cm, what is the greatest integer number of centimeters that could be the third side of this triangle?

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