
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 the function $f(x)=\frac{2x+3}{3x}$, and the sequence $\{a\_n\}$ satisfies $a\_1=1$, $a\_{n+1}=f(\frac{1}{a\_n})$, $n∈N^{*}$,
(1) Find the general term formula of the sequence $\{a\_n\}$;
(2) Let $T\_n=a\_1a\_2-a\_2a\_3+a\_3a\_4-a\_4a\_5+…-a\_{2n}a\_{2n+1}$, find $T\_n$;
(3) Let $b\_n=\frac{1}{a\_{n-1}a\_n}$ $(n≥2)$, $b\_1=3$, $S\_n=b\_1+b\_2+…+b\_n$, if $S\_n < \frac{m-2007}{2}$ holds for all $n∈N^{*}$, find the smallest positive integer $m$.

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