
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
How many degrees are there in the measure of angle $P$?

[asy]
size (6cm);
pair A,B,C,D,E,F;

A=(0,0);
B=(1,-1);
C=(3,-1);
D=(4,0);
E=(3,2);
F=(1,2);

draw (A--B--C--D--E--F--A, linewidth(1));

label("$P$", D, NE);
label("$135^\circ$", shift(0,-0.6) * A);
label("$120^\circ$", B, S);
label("$105^\circ$", C, S);
label("$150^\circ$", E, N);
label("$110^\circ$", F, N);
draw(anglemark(E,D,C), blue);
[/asy]

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