
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 $a$ and $b$ are positive real numbers, and for any $x \in (0, +\infty)$, the inequality $(a+b)x-1 \leq x^2$ always holds.  
(1) Find the minimum value of $\frac{1}{a} + \frac{1}{b}$;  
(2) Determine the position of point $P(1, -1)$ relative to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ and explain the reason.

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