
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
We know that the multiplication rule of powers with the same base is: $a^{m}\cdot a^{n}=a^{m+n}$ (where $a\neq 0$, $m$, $n$ are positive integers). Similarly, we define a new operation for any positive integers $m$ and $n$: $h(m+n)=h(m)\cdot h(n)$. If $h(1)=k$ ($k\neq 0$), then $h(n)\cdot h(2023)=$______ (expressed in an algebraic expression involving $n$ and $k$, where $n$ is a positive integer).

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