
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
Calculate or simplify the following expressions:

(1) $(1)\lg 5(\lg 8+\lg 1000)+{\left(\lg {2}^{ \sqrt{3}}\right)}^{2} $;

(2) Given $a-a^{-1}=2$, find the value of $\dfrac{({{a}^{3}}+{{a}^{-3}})({{a}^{2}}+{{a}^{-2}}-3)}{{{a}^{4}}-{{a}^{-4}}}$.

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