
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 is defined by \( a_0 = \frac{1}{3} \) and \( a_n = 1 + (a_{n - 1} - 1)^2 \). Compute
\[
a_0 a_1 a_2 \dotsm.
\]

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