
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
Using 14 matchsticks of equal length to form an isosceles triangle, where no matchsticks are allowed to be left over, overlapped, or broken, calculate the total number of different triangles that can be formed.

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