
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
Simplify first, then evaluate: $\left(\dfrac{a+2}{a^{2}-2a}+\dfrac{8}{4-a^{2}}\right)\div \dfrac{a^{2}-4}{a}$, where $a$ satisfies the equation $a^{2}+4a+1=0$.

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