
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
(Ⅰ) Given $2^x + 2^{-x} = 5$, find the value of $4^x + 4^{-x}$;  
(Ⅱ) Simplify $2( 32 \times \sqrt {3})^{6}+( \sqrt {2 \sqrt {2}})^{ \frac {4}{3}}-4( \frac {16}{49})^{- \frac {1}{2}}- 42 \times8^{0.25}+(-2005)^{0}$.

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