
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
A factory produced an original calculator that performs two operations:

- the usual addition +
- the operation $\circledast$

We know that for any natural number $a$:

$$
\text { (i) } a \circledast a=a \quad \text { e (ii) } a \circledast 0=2 a
$$

and for any four natural numbers $a, b, c,$ and $d$:

$$
\text { (iii) }(a \circledast b)+(c \circledast d)=(a+c) \circledast(b+d) \text {. }
$$

What are the results of the operations $(2+3) \circledast(0+3)$ and $1024 \circledast 48$?

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