
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 plank of wood has one end, \( A \), against a vertical wall. Its other end, \( B \), is on horizontal ground. When end \( A \) slips down \( 8 \text{ cm} \), end \( B \) moves \( 4 \text{ cm} \) further away from the wall. When end \( A \) slips down a further \( 9 \text{ cm} \), end \( B \) moves a further \( 3 \text{ cm} \) away from the wall. Find the length of the plank.

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