
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
Define a new operation "▽": For any rational numbers $x$ and $y$, $x$▽$y=m^{2}x+ny-1$ (where $m$ and $n$ are constants). For example, $4$▽$3=m^{2}\times 4+n\times 3-1=4m^{2}+3n-1$. If $2$▽$3=3$, then the value of $6$▽$9$ is ______.

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