
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 any rational numbers $x$, $y$, define the operation as follows: $x \triangle y = ax + by + cxy$, where $a$, $b$, $c$ are given numbers, and the right side of the equation involves the usual addition and multiplication of numbers. For example, when $a=1$, $b=2$, $c=3$, $1 \triangle 3 = 1 \times 1 + 2 \times 3 + 3 \times 1 \times 3 = 16$. It is known that the newly defined operation satisfies the conditions $1 \triangle 2 = 3$, $2 \triangle 3 = 4$, and there exists a non-zero number $d$ such that for any rational number $x \triangle d = x$. Find the values of $a$, $b$, $c$, $d$.

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