
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 real numbers $x, y$, define the operation $x * y = ax + by + cxy$, where $a, b, c$ are constants, and the operations on the right side of the equation are the usual addition and multiplication. It is already known that $1 * 2 = 4$, $2 * 3 = 6$, and there exists a non-zero real number $m$ such that for any real number $x$, $x * m = x$. Find the value of $m$.

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