
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 $\left\{a_{n}\right\}$ is defined as follows: $a_{1}=0, a_{2}=1, a_{n}=\max_{1 \leq i \leq n-1}\left\{a_{i}+a_{n-i}+i\right\}$. Determine the general term of the sequence $\left\{a_{n}\right\}$.

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