
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 $F$ be the left focus of the hyperbola $x^{2}-\frac{y^{2}}{3}=1$. A straight line $AB$ passes through $F$ and intersects the hyperbola at points $A$ and $B$. Tangents to the hyperbola are drawn at points $A$ and $B$, denoted as $l_{1}$ and $l_{2}$ respectively, and these tangents intersect at point $M$. 

(1) Find the angle between vector $MF$ and line $AB$.  
(2) Find the minimum area of triangle $\triangle MAB$.

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