
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
Let  $f: \mathbb{R} \rightarrow \mathbb{R}$  be a continuous function with the following property: for all  $\alpha \in \mathbb{R}_{>0}$ , the sequence  $(a_n)_{n \in \mathbb{N}}$  defined as  $a_n = f(n\alpha)$  satisfies  $\lim_{n \to \infty} a_n = 0$ . Is it necessarily true that  $\lim_{x \to +\infty} f(x) = 0$ ?

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