
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
The diagram below shows a pentagon (made up of region \( A \) and region \( B \)) and a rectangle (made up of region \( B \) and region \( C \)) that overlaps. The overlapped region \( B \) is \(\frac{3}{16}\) of the pentagon and \(\frac{2}{9}\) of the rectangle. If the ratio of region \( A \) of the pentagon to region \( C \) of the rectangle is \(\frac{m}{n}\) in its lowest term, find the value of \( m+n \).

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