
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
Find all real numbers $\lambda$ for which there does not exist an infinite sequence of positive terms $\left\{a_{n}\right\}$ satisfying
$$
a_{n} + 1 \leqslant \sqrt[n]{\lambda} a_{n-1} \quad (n \geq 2)
$$
for all $n$.

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