
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
Let the sequence $\{a_{n}\}$ satisfy ${a_1}=\frac{2}{5}$, and ${a_{n+1}}={a_n}+{a_n}^2$, $n\in N^{*}$. Let $S=\frac{1}{{{a_1}+1}}+\frac{1}{{{a_2}+1}}+…+\frac{1}{{{a_{2020}}+1}$. If $S\in \left(t,t+1\right)$, then the integer $t=$____.

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