
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
Provide an example of a function \( f(x) \) that satisfies all three of the following conditions:

- The domain of \( f(x) \) is the set of all real numbers \(\mathbb{R}\).
- For any \( b \in \mathbb{R} \), the equation \( f(x) = b \) has exactly one solution.
- For any \( a > 0 \) and any \( b \in \mathbb{R} \), the equation \( f(x) = a x + b \) has at least two solutions.

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