
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 the sequence $\{a_n\}$ with the general term formula $$a_{n}= \begin{cases} \left.\begin{matrix}-n, & n\leq4 \\ \sqrt {n^{2}-4n}-n, & n>4\end{matrix}\right.\end{cases}(n\in\mathbb{N}^*)$$, evaluate the limit of $a_n$ as $n$ approaches positive infinity.

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