
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
The focus of the parabola $y^{2}=2ax(a > 0)$ is $F$, and its directrix intersects with the hyperbola $\dfrac {y^{2}}{4}- \dfrac {x^{2}}{9}=1$ at points $M$ and $N$. If $\angle MFN=120^{\circ}$, then $a=$ ______.

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