
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 parabola is given by the equation $y=ax^{2}(a > 0)$. A line passing through its focus $F$ intersects the parabola at points $A$ and $B$. If the lengths of line segments $AF$ and $BF$ are $m$ and $n$ respectively, find the value of $\frac{mn}{m+n}$.

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