
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 line with a slope of $1$ intersects the parabola $y=ax^{2}(a > 0)$ at points $A$ and $B$. The distance from the midpoint $C$ of line segment $AB$ to the $y$-axis is $1$. Determine the distance from the focus of the parabola to its directrix.

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