
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 function value of $f$ at $n=1$ is ____.  
(2) Let $k=5$, and when $n \leq 5$, $1 \leq f(n) \leq 2$, then the number of different functions $f$ is ____.

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