
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 the sum of the first $n$ terms of the sequence $\{a\_n\}$ is $S\_n$, and $S\_n= \frac {3}{2}n^{2}+ \frac {1}{2}n$, the increasing geometric sequence $\{b\_n\}$ satisfies: $b\_1+b\_4=18$, $b\_2⋅b\_3=32$.

1. Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\}$.
2. If $c\_n=a\_n⋅b\_n$, $n∈N$, find the sum of the first $n$ terms, $T\_n$, of the sequence $\{C\_n\}$.

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