
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
In the set of real numbers $\mathbf{R}$, define the operation $*$ satisfying:
(i) $x * 0 = 1$ (for any $x \in \mathbf{R}$).
(ii) $(x * y) * z = (z * x y) + z$ (for any $x, y, z \in $\mathbf{R}$).
Find $31 * 32$.

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