
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
A teenager can accurately memorize the value of $\pi$ to 200 decimal places. Even more miraculously, when asked about a specific decimal place, the teenager can accurately state the digit at that position. Let the digit at the $n$th decimal place of $\pi$ be denoted as $y$. Then, $y$ is a function of $n$, denoted as $y = f(n)$, where $n \in \mathbb{N}^{*}$. Determine the following:  
(1) The range of $y = f(n)$ is _______;  
(2) The number of intersection points between the functions $y = f(n)$ and $y = n^{2}$ is _______.

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