
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
【Reading comprehension】Read the following method of solving equations and then solve the problem.<br/>When solving the equation system $\left\{\begin{array}{l}{16x+14y=170①}\\{14x+16y=130②}\end{array}\right.$, it is very complicated to consider elimination directly, but using the following method makes it easy.<br/>Solution: Add ① and ②, $30x+30y=300$,<br/>which means $x+y=10$ ③<br/>Subtract ② from ①, $2x-2y=40$,<br/>which means $x-y=20$ ④<br/>Solve ③ and ④ simultaneously, we get $\left\{\begin{array}{l}{x+y=10①}\\{x-y=20②}\end{array}\right.$</td><td width="284">Solving, we get $\left\{\begin{array}{l}{x=15}\\{y=-5}\end{array}\right.$<br/>Therefore, the solution to the original equation system is $\left\{\begin{array}{l}{x=15}\\{y=-5}\end{array}\right.$</td></tr></tbody></table>​【Understanding application】(1) From the system of linear equations $\left\{\begin{array}{l}{2x+3y=6}\\{3x+2y=4}\end{array}\right.$, we can obtain $x+y=$______; $x-y=\_\_\_\_\_\_.$<br/>(2) Solve the equation system $\left\{\begin{array}{l}{2024x+2025y=2023}\\{2022x+2023y=2021}\end{array}\right.$;<br/>【Extension and enhancement】(3) For real numbers $x$ and $y$, a new operation is defined: $x*y=ax+by+c$, where $a$, $b$, $c$ are constants, for example: $5*6=5a+6b+c$. Given $2*4=15$, $3\cdot 7=27$, then $1*1=\_\_\_\_\_\_$.

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