
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
In triangle \(ABC\), the sides are known: \(AB = 5\), \(BC = 8\), \(AC = 7\). On the bisector of angle \(A\) (inside the triangle), a point \(O\) is chosen such that the areas of triangles \(AOB\), \(AOC\), and \(BOC\), taken in that order, form an arithmetic progression. Find this progression.

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