
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
Side  $AB$  of triangle  $ABC$  was divided into  $n$  equal parts (dividing points  $B_0 = A, B_1, B_2, ..., B_n = B$ ), and side  $AC$  of this triangle was divided into  $(n + 1)$  equal parts (dividing points  $C_0 = A, C_1, C_2, ..., C_{n+1} = C$ ). Colored are the triangles  $C_iB_iC_{i+1}$  (where  $i = 1,2, ..., n$ ). What part of the area of the triangle is painted over?

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