
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 $x$ and $y$ are rational numbers, a new operation ※ is defined such that $x$※$y=xy+1$. Find:<br/>
$(1)$ The value of $2$※$4$;<br/>
$(2)$ The value of $(1$※$4)$※$(-2)$;<br/>
$(3)$ Explore the relationship between $a$※$(b+c)$ and $a$※$b+a$※$c$, and express them using an equation.

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