
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
Given the parabola $C: y=ax^{2}(a > 0)$, the distance from the focus to the directrix is $\dfrac{1}{4}$, and two points $A(x_{1},y_{1})$, $B(x_{2},y_{2})$ on $C$ are symmetric about the line $y=x+m$, and $x_{1}x_{2}=-\dfrac{1}{2}$. Find the value of $m$.

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