
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 piece of paper in the shape of an isosceles triangle is folded such that the vertex $A$ of its base is brought to the midpoint of side $BC$. As a result, one endpoint of the crease (folding line) divides the side $AC$ in a ratio of $p: q$. In what ratio does the other endpoint of the crease divide the base $AB$?

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