
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
Given the function $f(x) = \frac{a \cdot 2^x - 1}{2^x + 1}$ (where $a$ is a real number),

(1) Discuss the evenness and oddness of the function $y = f(x)$ based on different values of $a$ and explain the reasons;

(2) If $1 \leq f(x) \leq 3$ for any $x \geq 1$, find the range of values for $a$.

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