
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
The vertices of a convex polygon with  $n\geqslant 4$  sides are coloured with black and white. A diagonal is called *multicoloured* if its vertices have different colours. A colouring of the vertices is *good* if the polygon can be partitioned into triangles by using only multicoloured diagonals which do not intersect in the interior of the polygon. Find the number of good colourings. 

*Proposed by S. Berlov*

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