
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 $\{a_n\}$ that satisfies $a_n+a_{n+1}=(-1)^{\frac{n(n+1)}{2}}n$, and $S_n$ is the sum of its first $n$ terms. If $S_{2015}=-1007-b$, and $a_1b > 0$, then the minimum value of $\dfrac{1}{a_1}+ \dfrac{2}{b}$ is \_\_\_\_\_\_.

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