
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 the set $W$ consist 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 $a_n \leq M$ for all positive integers $n$.

Among the following sequences: (1) $\{n^2+1\}$; (2) $\left\{ \frac {2n+9}{2n+11} \right\}$; (3) $\left\{2+ \frac {4}{n}\right\}$; (4) $\left\{1- \frac {1}{2^{n}}\right\}$, the ones that belong to set $W$ are \_\_\_\_\_\_.

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