
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 $k \in \mathbb{N}^*$, let the function $f: \mathbb{N}^* \rightarrow \mathbb{N}^*$ satisfy: for any positive integer $n$ greater than $k$, $f(n) = n - k$.

(1) Let $k=1$, then the value of the function $f(x)$ at $n=1$ is $\boxed{a}$ (where $a$ is a positive integer).

(2) Let $k=4$, and when $n \leq 4$, $2 \leq f(n) \leq 3$, then the number of different functions $f$ is $\boxed{16}$.

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