
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
Given a triangle split into smaller sections with angles as shown:
- $m\angle 1 = 34^\circ$
- $m\angle 2 = 53^\circ$
- $m\angle 3 = 27^\circ$
Calculate the measure of $m\angle 4$ within the triangle.

[asy]
draw((0,0)--(4,8)--(10,0)--cycle,linewidth(1));
draw((0,0)--(5,3)--(10,0),linewidth(1));
label("2",(1,1.2));
label("1",(4,7.75),S);
label("4",(5,3),S);
label("3",(8,1.2));
[/asy]

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