
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]


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Konstantin traveled the 180-meter distance from school to home by taking 300 steps, with each step being no longer than \(a\) cm, and the sum of the lengths of any two steps was greater than the length of any other step. What values can the number \(a\) take under these conditions?

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