
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
Let $M$ be a point inside $\triangle ABC$, and the area of $\triangle ABC$ is $2$. Define $f(M)=(m,n,p)$, where $m$, $n$, $p$ are the areas of $\triangle MBC$, $\triangle MCA$, $\triangle MAB$ respectively. If a moving point $P$ inside $\triangle ABC$ satisfies $f(P)=(1,x,y)$, calculate the minimum value of $\dfrac{1}{x}+ \dfrac{4}{y}$.

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