
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) Given that $a^x - a^{-x} = 2$, find the value of $a^{2x} + a^{-2x}$.
(2) Evaluate: $2\log_{2} \sqrt {8} - \log_{2} \frac {32}{9} - 2\log_{2}3 + 2^{{\log_{2}3}}$.

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