
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 the curve $f(x)=\frac{x^2}{a}-1 (a > 0)$.

$\quad\quad\quad\;\;(1)$ If $a=1$, find the coordinates of the point $P$ where the tangent line to the curve $f(x)$ is parallel to the line $x-2y-2=0$.

$\quad\quad\quad\;\;(2)$ Let $l$ be the equation of the tangent line to the curve $f(x)$ at $x=1$. Find the minimum value of the area of the triangle formed by $l$ and the two coordinate axes.

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