
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 triangle $ABC$, $\angle BAC = 90^\circ$. Additionally, there is a point $D$ on $BC$, creating triangle $ABD$, where $\angle ABD = 2y^\circ$ and $\angle BAD = y^\circ$. Determine the value of $y$.

[asy]
size(100);
draw((0,1)--(0,0)--(1,0));
draw((0,0)--(.5,.866));
draw((0,.1)--(.1,.1)--(.1,0));
label("$A$",(0,1),N); label("$B$",(0,0),SW); label("$C$",(1,0),E); label("$D$",(.5,.866),NE);
label("$2y^\circ$",(0.15,0.4),N);
label("$y^\circ$",(0.25,-0.02),N);
[/asy]

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