
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
Proposition P: The function $f(x) = x^2 - 2ax + 2$ has exactly one zero point within the interval $[0, 1]$; Proposition Q: The function $y = a^x$ $(a > 0, a \neq 1)$ is an increasing function on $\mathbb{R}$.
(1) If $f(1) = 0$, find the value of $a$;
(2) If "P or Q" is true and "P and Q" is false, determine the range of values for $a$.

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