
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 $a\_1 = a$ ($a \neq 1$ and $a \neq -3$), $a\_2 = 3$, and $a\_n = 2a\_{n-1} + 3a\_{n-2}$ ($n \geq 3$).
(I) Find the general terms for the sequences $\{a\_{n+1} + a\_n\}$ and $\{a\_{n+1} - 3a\_n\}$;
(II) If the sequence $\{a\_n\}$ is strictly increasing, find the range of possible values for $a$.

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