
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 $x$ and $y$, define a mathematical operation $\Delta$ such that $x\ \Delta\ 0 = x + 2$, $x\ \Delta\ y = y\ \Delta\ x$, and $(x + 1)\ \Delta\ y = (x\ \Delta\ y) + y + 2$. Determine the result of $7\ \Delta\ 3$.

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