
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. Compute: $( \sqrt {1000})^{- \frac {2}{3}}×( \sqrt[3]{10^{2}})^{ \frac {9}{2}}$;
2. Compute: $\lg 20+\log _{100}25$;
3. Find the domain of the function: $f(x)= \sqrt {1-\log _{2}(4x-5)}$.

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