
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: \( a_{0}=a_{1}=0, a_{2}=1 \), and for \( n \geqslant 3 \), \( a_{n}=6 a_{n-1}-11 a_{n-2}+6 a_{n-3} \). Find the generating function for the sequence \( \{a_{n}\}_{n \geqslant 0} \).

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