
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 a sequence {a\_n} that satisfies a\_1 = 1 and a\_{n+1} = f($$\frac{1}{a\_n}$$) for all n ∈ N+.

1. Find the general formula for the terms of the sequence {a\_n}.
2. Let b\_n = $$\frac{1}{a\_{n-1} \cdot a\_{n+1}}$$ for n ≥ 2, b\_1 = 3, and S\_n = b\_1 + b\_2 + ... + b\_n. If S\_n < $$\frac{m - 2007}{2}$$ holds true for all n ∈ N+, find the smallest positive integer value of m.

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