
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 first term $a\_1=1$ and common difference $d \neq 0$. It is known that $a\_2$, $a\_5$, and $a\_{14}$ form a geometric sequence.
(I) Find the general term of the sequence $\{a\_n\}$;
(II) Let $c\_n = \frac{1}{a\_n a\_{n+1}}$, 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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