
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
Explain a method to multiply two numbers using only addition, division by 2, and multiplication by 2, as illustrated by the following example of multiplying 97 by 23. The method involves the following steps:

1. Write the two numbers at the top of two columns.
2. In the first column, repeatedly divide the number by 2 (discarding the remainder) until you reach 1.
3. In the second column, repeatedly multiply the number by 2 the same number of times.

For example:

| 97 | 23 |
| ---: | :---: |
| 48 | 46 |
| 24 | 92 |
| 12 | 184 |
| 6 | 368 |
| 3 | 736 |
| 1 | 1472 |
| | 2231 |

Next, cross out the entries in the second column corresponding to even numbers in the first column, and sum the remaining numbers:

The numbers not crossed out are 23, 736, and 1472. Adding these together gives the product 2231.

Why does this method work?

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