
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) Given $5^a = 3$ and $5^b = 4$, find $a$ and $b$. Also, express $\log_{25}12$ in terms of $a$ and $b$.  
(2) If $x^{\frac{1}{2}} + x^{-\frac{1}{2}} = 5$, find the value of $\frac{x}{x^2 + 1}$.

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