
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 $x$ and $y$, define the operation $x*y=ax+by+cxy$, where $a$, $b$, and $c$ are constants, and the operations on the right side of the equation are the usual addition and multiplication. Given that $1*2=3$ and $2*3=4$, and there exists a non-zero constant $m$ 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