
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
Find all values of the parameter \( a \) for which the roots \( x_{1} \) and \( x_{2} \) of the equation

\[ 2x^{2} - 2016(x - 2016 + a) - 1 = a^{2} \]

satisfy the double inequality \( x_{1} < a < x_{2} \).

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