
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
Here are the steps of a numerical trick:

(i) Choose any number.

(ii) Multiply it by 6.

(iii) Subtract 21 from the result.

(iv) Divide the new result by 3.

(v) Subtract twice the number you initially chose from this last result.

(a) Try this sequence of five steps three times, starting with a different number each time. What was the result of your experiment?

(b) Next, using the letter \( x \) to represent the number you chose in the first step, show why the results from part (a) are not just a coincidence, but a mathematical fact.

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