
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
Given a regular triangle is entirely painted black, with each transformation consisting of dividing the black triangle into four smaller congruent triangles and painting the middle smaller triangle white, determine the portion of the triangle that remains black after five transformations.

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