
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 $\triangle ABC$ have sides $a$, $b$, $c$ opposite to the internal angles $A$, $B$, $C$, respectively, and the height $h$ on side $BC$ is $h=\frac{\sqrt{3}}{4}a$.<br/>$(1)$ If $A=\frac{π}{2}$, find $B$;<br/>$(2)$ Given that angles $B$ and $C$ in $\triangle ABC$ are acute angles, find the minimum value of $\tan B+4\tan C$.

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