
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 that $F$ is the focus of the parabola $y^{2}=ax(a > 0)$. The coordinates of point $M$ are $(4,0)$. A line with slope $k_{1}$ passing through point $F$ intersects the parabola at points $A$ and $B$. Extending $AM$ and $BM$ to intersect the parabola at points $C$ and $D$ respectively, let the slope of line $CD$ be $k_{2}$, and $k_{1}= \sqrt {2}k_{2}$. Find the value of $a$.

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