
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  $(a_n)_{n\in\mathbb N}$  be a sequence, given by the recurrence:  $$ ma_{n+1}+(m-2)a_n-a_{n-1}=0 $$  where  $m\in\mathbb R$  is a parameter and the first two terms of  $a_n$  are fixed known real numbers. Find  $m\in\mathbb R$ , so that  $$ \lim_{n\to\infty}a_n=0 $$  *Proposed by Laurențiu Modan*

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