
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 an arithmetic sequence {a\_n} with common difference d > 0 and the sum of the first n terms as S_n. The sequence satisfies the conditions a_2 * a_3 = 45 and a_1 + a_4 = 14.
(I) Find the general term formula for the sequence {a\_n} and the sum of the first n terms, S_n.
(II) Let b_n = S_n / (n + c). If the sequence {b_n} is also an arithmetic sequence, determine the non-zero constant c and find the sum of the first n terms, T_n, for the sequence {1 / (b_n * b_{n+1})}.

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