
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
The lengths of the sides of an acute triangle form an arithmetic progression with a common difference of 5 cm. Find the largest number with the property that the length of the longest side of any triangle of this type is greater than this number.

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