
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 \( G(0) = 1 \), \( G(1) = 4 \), and for \( n \ge 2 \),
\[
G(n) = 3G(n - 1) - 2G(n - 2)
\]
Find the sum 
\[
\sum_{n=0}^5 G(n).
\]

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