
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
We know that: $\dfrac {n+p}{m(n+q)}= \dfrac {p}{q}- \dfrac {1}{n}- \dfrac {p-q}{q}- \dfrac {1}{n+q}$.  
Given a sequence $\{a_n\}$, where $a_1=1$ and $a_n=2a_{n-1}+ \dfrac {n+2}{n(n+1)}$ for $n\geqslant 2, n\in\mathbb{N}^*$, find the general formula for the sequence $\{a_n\}$, $a_n=$ ______.

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