
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 \( a \mathrm{~cm}, 2 \mathrm{~cm} \) and \( b \mathrm{~cm} \), 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}
user