
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
Calculate the following values:  
(1) If $x^{ \frac {1}{2}}+x^{- \frac {1}{2}}=3$, find the value of $x+x^{-1}$;  
(2) Let $\lg 2=a$, $\lg 3=b$, calculate the value of $\log_{5}12$.

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