
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
Let \( n \) be an integer with \( n \geq 3 \). Consider all dissections of a convex \( n \)-gon into triangles by \( n-3 \) non-intersecting diagonals, and all colorings of the triangles with black and white so that triangles with a common side are always of a different colour. Find the least possible number of black triangles.

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