
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, $\angle ABC = 90^\circ$. Label the smaller angle at $A$ as $3x^\circ$ and the angle at $B$ next to $A$ as $4x^\circ$ - 10. Find the value of $x$.

[asy]
size(100);
draw((0,1)--(0,0)--(1,0));
draw((0,0)--(.8,.6));
draw((0,.1)--(.1,.1)--(.1,0));
label("$A$",(0,1),N); label("$B$",(0,0),SW); label("$C$",(1,0),E); label("$D$",(.8,.6),NE);

label("$3x^\circ$",(.15,.2)); label("$4x^\circ - 10$",(.45,-.02),S);

[/asy]

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