
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 $y=2px^2$ ($p > 0$) with focus $F$, and point $P\left( 1,\dfrac{1}{4} \right)$ on the parabola. A line $PQ$ is drawn perpendicular to the directrix of the parabola from point $P$, with the foot of the perpendicular being point $Q$. If the directrix of the parabola intersects its axis of symmetry at point $M$, then the area of quadrilateral $PQMF$ is $\boxed{\dfrac{13}{8}}$.

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