
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 $M$ is a point inside $\triangle ABC$ (excluding the boundary) with an area of 1, and the areas of $\triangle MBC$, $\triangle MCA$, and $\triangle MAB$ are $x$, $y$, and $z$ respectively, calculate the minimum value of $\frac {1}{x+y} + \frac {x+y}{z}$.

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