
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 be given a triangle  $ABC$  and points  $D,M,N$  belong to  $BC,AB,AC$ , respectively. Suppose that  $MD$  is parallel to  $AC$  and  $ND$  is parallel to  $AB$ . If  $S_{\vartriangle BMD} = 9$  cm  $^2, S_{\vartriangle DNC} = 25$  cm $^2$ , compute  $S_{\vartriangle AMN}$ ?



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