
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 $a\_1=1$, $a_{n+1}=a\_n^{2}+a\_n$, using $[x]$ to denote the largest integer not greater than $x$, determine the value of $\left[ \frac {1}{a\_1+1}+ \frac {1}{a\_2+1}+...+ \frac {1}{a_{2015}+1}\right]$ .

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