
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 the diagram, $\triangle ABC$ is right-angled at $A$, with $AB=60$ and $AC=160.$ The point $M$ is the midpoint of $BC.$ Determine the length of $AM.$ 
[asy]
pair A, B, C, M;
B=(0,0);
A=(180,0);
C=(180,240);
M=(180,120);
draw(A--B--C--A--M);
label("B", B, SW);
label("A", A, SE);
label("C", C, NE);
label("M", M, NW);
label("60", (A+B)/2, S);
label("160", (A+C)/2, E);
[/asy]

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