
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
On  $\vartriangle ABC$  let  $D$  be a point on side  $\overline{AB}$ ,  $F$  be a point on side  $\overline{AC}$ , and  $E$  be a point inside the triangle so that  $\overline{DE}\parallel  \overline{AC}$  and  $\overline{EF} \parallel \overline{AB}$ . Given that  $AF = 6, AC = 33, AD = 7, AB = 26$ , and the area of quadrilateral  $ADEF$  is  $14$ , nd the area of  $\vartriangle ABC$ .

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