
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
A sequence of numbers  $ a_1, a_2, a_3, ...$  satisfies

(i)  $ a_1 \equal{} \frac{1}{2}$ 
(ii)  $ a_1\plus{}a_2 \plus{} \cdots \plus{} a_n \equal{} n^2 a_n \ (n \geq 1)$ 

Determine the value of  $ a_n \ (n \geq 1)$ .

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