
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
(1) Evaluate  $ \int_0^1 xe^{x^2}dx$ .

(2) Let  $ I_n\equal{}\int_0^1 x^{2n\minus{}1}e^{x^2}dx$ . Express  $ I_{n\plus{}1}$  in terms of  $ I_n$ .

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