
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  $ABCD$  be a trapezoid of bases  $AB$  and  $CD$  . Let  $O$  be the intersection point of the diagonals  $AC$  and  $BD$ . If the area of the triangle  $ABC$  is  $150$  and the area of the triangle  $ACD$  is  $120$ , calculate the area of the triangle  $BCO$ .

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