
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
Triangle  $ABC$  has  $AB = 4$ ,  $AC = 5$ , and  $BC = 6$ .  An angle bisector is drawn from angle  $A$ , and meets  $BC$  at  $M$ .  What is the nearest integer to  $100 \frac{AM}{CM}$ ?

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