
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
Evaluate or simplify:  
1. $\log_2 \sqrt{2}+\log_9 27+3^{\log_3 16}$;  
2. $0.25^{-2}+\left( \frac{8}{27} \right)^{-\frac{1}{3}}-\frac{1}{2}\lg 16-2\lg 5+\left( \frac{1}{2} \right)^{0}$.

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