
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
In rectangle \( J K L M \), the bisector of angle \( K J M \) cuts the diagonal \( K M \) at point \( N \). The distances between \( N \) and sides \( L M \) and \( K L \) are \( 8 \) cm and \( 1 \) cm respectively. The length of \( K L \) is \( (a+\sqrt{b}) \) cm. What is the value of \( a+b \)?

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