
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
Let the sum of the first $n$ terms of an arithmetic sequence $\{a_n\}$ be $S_n$, and $S_5=a_5+a_6=25$.  
(I) Find the general formula for $\{a_n\}$.  
(II) If the inequality $2S_n+8n+27 > (-1)^n k(a_n+4)$ holds for all positive integers $n$, find the range of the real number $k$.

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