
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 ball is propelled from corner \( A \) of a square snooker table of side 2 metres. After bouncing off three cushions as shown, the ball goes into a pocket at \( B \). The total distance travelled by the ball is \( \sqrt{k} \) metres. What is the value of \( k \)? (Note that when the ball bounces off a cushion, the angle its path makes with the cushion as it approaches the point of impact is equal to the angle its path makes with the cushion as it moves away from the point of impact.)

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