
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
Find the area of triangle $ABC$ below which is a right triangle with a $45^\circ$ angle at $A$.

[asy]
unitsize(1inch);
pair P,Q,R;
P = (0,0);
Q= (5,0);
R = (0,5);
draw (P--Q--R--P,linewidth(0.9));
label("$A$",P,S);
label("$B$",Q,S);
label("$C$",R,W);
label("$5$",Q/2,S);
label("$5$",R/2,W);
label("$45^\circ$",(-0.2,0.2),S);
[/asy]

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