
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 a sequence $\{a_n\}$ where $a_1=1$, and for $k=1,2,3,\ldots,$ the recursive formulas are given as $a_{2k}=a_{2k-1}+(-1)^k$ and $a_{2k+1}=a_{2k}+3^k$.  
(I) Calculate $a_3$ and $a_5$;  
(II) Find the general term formula for the sequence $\{a_n\}$.

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