
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 sequence $\{a\_n\}$ is an arithmetic sequence, with $a\_1=5$, $a\_2=9$, and the sum of the first $n$ terms of the sequence $\{b\_n\}$ is $S\_n= \frac {2}{3}b\_n+ \frac {1}{3}$.
(I) Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\}$;
(II) If $c\_n=a\_n|b\_n|$, find the sum of the first $n$ terms of the sequence $\{c\_n\}$, denoted as $T\_n$.

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