
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
$(1)$ Simplify and find the value of: ${4}^{log_{2}3}-log_{3}7 \cdot log_{7}9+log_{18}6+log_{18}3$;<br/>$(2)$ Given ${x}^{\frac{1}{2}}+{x}^{-\frac{1}{2}}=\sqrt{5}$, find the value of $x^{2}+x^{-2}$.

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