
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
A triangle with sides $a,b,c$ is called a good triangle if $a^2,b^2,c^2$ can form a triangle. Determine how many of the triangles with angles $40^{\circ}, 60^{\circ}, 80^{\circ}$; $10^{\circ}, 10^{\circ}, 160^{\circ}$; $110^{\circ}, 35^{\circ}, 35^{\circ}$; $50^{\circ}, 30^{\circ}, 100^{\circ}$; $90^{\circ}, 40^{\circ}, 50^{\circ}$; $80^{\circ}, 20^{\circ}, 80^{\circ}$ are good.

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