
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 set $W$ be composed of sequences $\{a\_n\}$ that satisfy the following two conditions:
\[① \frac{a\_n + a_{n+2}}{2} < a_{n+1};\] \[②\] There exists a real number $M$ such that $a\_n \leqslant M$ $(n$ is a positive integer$)$.
Identify the number(s) of the following sequences that belong to set $W$:
\[\text{(1) } \{n^{2}+1\};\] \[\text{(2) } \left\{ \frac{2n+9}{2n+11} \right\};\] \[\text{(3) } \left\{2 + \frac{4}{n} \right\};\] \[\text{(4) } \left\{1 - \frac{1}{2^{n}} \right\}.\]

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