
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 $\triangle ABC$ and point $D$ on segment $BC$ (excluding the endpoints), if $\overrightarrow{AD}=m\overrightarrow{AB}+n\overrightarrow{AC}$, determine the minimum value of $\frac{1}{m}+\frac{4}{n}$.

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