
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
 $ABCD$  is a rectangle.  $E$  is a point on  $AB$  between  $A$  and  $B$ , and  $F$  is a point on  $AD$  between  $A$  and  $D$ . The area of the triangle  $EBC$  is  $16$ , the area of the triangle  $EAF$  is  $12$  and the area of the triangle  $FDC$  is 30. Find the area of the triangle  $EFC$ .

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