
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
Let \( c > 0 \) be a positive real number. We define the sequence \( \left(x_{n}\right) \) by \( x_{0} = 0 \) and
\[ x_{n+1} = x_{n}^{2} + c \]
for each \( n \geq 0 \). For which values of \( c \) is it true that \( \left| x_{n} \right| < 2016 \) for all \( n \)?

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