
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
Let  $\star$  be an operation defined in the set of nonnegative integers with the following properties: for any nonnegative integers  $x$  and  $y$ ,
(i)  $(x + 1)\star 0 = (0\star x) + 1$ (ii)  $0\star (y + 1) = (y\star 0) + 1$ (iii)  $(x + 1)\star (y + 1) = (x\star y) + 1$ .
If  $123\star 456 = 789$ , find  $246\star 135$ .

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