
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 following expression:
$$\left( \frac {2}{3} \right)^{0} + 2^{-2} \times \left( \frac {16}{9} \right)^{\frac {1}{2}} + (\lg 8 + \lg 125)$$;
2. Given that $a + a^{-1} = 5$, 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}
user