
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
Given that \( a_{0}=b_{0}=1 \) and \( a_{n}=a_{n-1}+2 b_{n-1} \), \( b_{n}=a_{n-1}+b_{n-1} \) for \( n=1,2, \cdots \), find the value of \( a_{1993}^{2}-2 b_{1993}^{2} \).

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