
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
In triangle  $ABC$ ,  $D$  is a point on  $AB$  between  $A$  and  $B$ ,  $E$  is a point on  $AC$  between  $A$  and  $C$ , and  $F$  is a point on  $BC$  between  $B$  and  $C$  such that  $AF$ ,  $BE$ , and  $CD$  all meet inside  $\triangle ABC$  at a point  $G$ . Given that the area of  $\triangle ABC$  is  $15$ , the area of  $\triangle ABE$  is  $5$ , and the area of  $\triangle ACD$  is  $10$ , compute the area of  $\triangle ABF$ .

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