
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
The sequence  $ (x_n)$  is defined by  $ x_1\equal{}1,x_2\equal{}a$  and  $ x_n\equal{}(2n\plus{}1)x_{n\minus{}1}\minus{}(n^2\minus{}1)x_{n\minus{}2}$   $ \forall n \geq 3$ , where  $ a \in N^*$ .For which value of  $ a$  does the sequence have the property that  $ x_i|x_j$  whenever  $ i<j$ .

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