
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
In an infinite sequence, \( a_{0} = c \) and

\[ a_{n} = 2 \left(a_{n-1} - 1 \right)^{2} \quad \text{for} \quad n = 1, 2, \ldots \]

Determine \( a_{n} \) as a function of \( c \) and \( n \).

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