
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 a sequence $\{a_n\}$ satisfying $a_{n+1} + 1 = \frac{a_n + 1}{2a_n + 3}$, and $a_1 \neq 1$, find the sum of the first 20 terms of the sequence $\left\{ \frac{2}{a_n+1} \right\}$.

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