
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
An octagon consists of 12 unit squares. One of the diagonals divides the octagon into two regions: one below the diagonal is a rectangle with a width of 3 units and the other containing two triangles, each having a base of 3 units and heights equivalent to the height of the rectangle. If the diagonal exactly bisects the area of the octagon, determine the ratio of the height of the rectangle to the total height of the octagonal area.
A) $\frac{1}{4}$
B) $\frac{2}{3}$
C) $\frac{1}{2}$
D) $\frac{3}{4}$
E) $\frac{3}{5}$

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