
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
(1) Calculate the value of $$\frac {2}{3}\lg8+\lg^{2}5+\lg2\cdot \lg50+\lg25$$;  
(2) Given $a+a^{-1}=5$, find the values of $a^{2}+a^{-2}$ and $$a^{ \frac {1}{2}}+a^{- \frac {1}{2}}$$.

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