
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. It is known that $1*2 = 4$, $2*3 = 6$. If there exists a non-zero real number $m$ such that for any real number $x$, $x*m = x$, determine the value of $m$.

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