
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 sequence $\{a\_n\}$ that satisfies the conditions: $a\_1=1$, $a\_{n+1}=2a\_n+1$
(1) Find the general term formula of the sequence $a\_n$
(2) Let $c\_n= \frac {2^{n}}{a\_n \cdot a\_{n+1}}$ and $T\_n=c\_1+c\_2+c\_3+...+c\_n$. Find $T\_n$.

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