
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
Given some triangles with side lengths \(a \,\text{cm}, 2 \,\text{cm}\) and \(b \,\text{cm}\), where \(a\) and \(b\) are integers and \(a \leq 2 \leq b\). If there are \(q\) non-congruent classes of triangles satisfying the above conditions, find the value of \(q\).

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