
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

Through the vertex \(B\) of triangle \(ABC\), a line \(\ell\) is drawn parallel to side \(AC\). The angle bisector of angle \(A\) intersects \(\ell\) at point \(A'\), and the angle bisector of angle \(C\) intersects \(\ell\) at point \(C'\). It is known that the area of triangle \(ABA'\) is \(50\%\) greater and the area of triangle \(CBC'\) is \(25\%\) greater than the area of triangle \(ABC\). The bisectors intersect at point \(O\). What fraction of the area of triangle \(AOC\) is the area of triangle \(ABC\)?

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