
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 $a_{n+1}+2= \frac {3a_{n}+4}{2a_{n}+3}$, and $a_{1}=1$. Let $b_{n}= \frac {a_{n}+1}{2}$, then the sum of the first 50 terms of the sequence $\{b_{n} \cdot b_{n+1}\}$ is $\_\_\_\_\_\_\_\_$.

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