
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 that $\{a\_n\}$ is an arithmetic sequence with a common difference $d \neq 0$, and $a\_2$, $a\_6$, $a\_{22}$ form a geometric sequence, $a\_4 + a\_6 = 26$; sequence $\{b\_n\}$ is a geometric sequence with a common ratio $q$ as a positive number, and $b\_3 = a\_2$, $b\_5 = a\_6$.
(I) Find the general terms of sequences $\{a\_n\}$ and $\{b\_n\}$;
(II) Find the sum of the first $n$ terms of the sequence $\{a\_n \cdot b\_n\}$, denoted as $T\_n$.

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