
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, $\angle ABC = 90^\circ$. A point D is placed on line AC such that $\angle DBA = 3x^\circ$ and $\angle DBC = 2x^\circ$. What is the value of $x$?

[asy]
size(100);
draw((0,1)--(0,0)--(1,0));
draw((0,0)--(1,0.6));
draw((0,.1)--(.1,.1)--(.1,0));
label("$A$",(0,1),N); label("$B$",(0,0),SW); label("$C$",(1,0),E); label("$D$",(1,0.6),NE);
label("$3x^\circ$",(.15,.2)); label("$2x^\circ$",(.75,.07),N);
[/asy]

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