
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
Through two vertices of a triangle, lines are drawn that divide it into three triangles and a quadrilateral.

a) Can the areas of all four parts be equal?

b) Which three of these parts can have equal areas? By how much does the area of the fourth part differ from them?

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