
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 $\{a_n\}$, where $a_1=\frac{1}{2}$, and $a_{n+1}=a_n^2+a_n$ for $n\in \mathbf{N}^*$, let $m=\frac{1}{a_1+1}+\frac{1}{a_2+1}+\cdots +\frac{1}{a_{2016}+1}$. Find the integer part of $m$.

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