
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
For an olympiad geometry problem, Tina wants to draw an acute triangle whose angles each measure a multiple of  $10^{\circ}$ . She doesn't want her triangle to have any special properties, so none of the angles can measure  $30^{\circ}$  or  $60^{\circ}$ , and the triangle should definitely not be isosceles.

How many different triangles can Tina draw? (Similar triangles are considered the same.)

*Proposed by Evan Chen*

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