
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
David has a very unique calculator that performs only two operations, the usual addition $(+)$ and another operation denoted by $*$, which satisfies:

(i) $a * a = a$,

(ii) $a * 0 = 2a$ and 

(iii) $(a * b) + (c * d) = (a + c) * (b + d)$,

for any integers $a$ and $b$. What are the results of the operations $(2 * 3) + (0 * 3)$ and $1024 * 48$?

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