
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 that $x + \frac{1}{x} = 3$, find the value of $x^2 + \frac{1}{x^2}$;
(2) Given that $a$, $b$, and $c$ are positive real numbers, and $a^x = b^y = c^z$, $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 0$, find the value of $abc$.

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