
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
A square's sides are each divided into $n$ and $m$ congruent segments on alternating opposite sides (with $n=6$ and $m=8$). Endpoints of one segment on a side divided into $n$ segments are joined to the square's center to form triangle $A$, and similarly, a segment from a side divided into $m$ segments forms triangle $B$. What is the ratio of the area of triangle $A$ to the area of triangle $B$?
A) $\frac{3}{4}$
B) $1$
C) $\frac{4}{3}$
D) $\frac{6}{8}$
E) $\frac{8}{6}$

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