
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 triangle is formed using sticks of lengths 13, 20, and 25 inches joined end-to-end. Pieces of different integral lengths are cut from each of the sticks so that the three remaining pieces no longer form a triangle. If the piece cut from the 13 inch stick is half the length of the piece cut from the 25 inch stick, and the piece cut from the 20 inch stick is 2 inches less than the piece cut from the 25 inch stick, find the smallest piece that can be cut from the 25 inch stick to make this happen.

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