
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
For all real numbers $r$ and $s$, define the mathematical operation $\#$ such that: $r \# 0 = r$, $r \# s = s \# r$, and $(r + 1) \# s = (r \# s) + s + 2$. Compute the value of $12 \# 6$.

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