
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 $ABC$ with $\angle BAC = 90^\circ$, let $D$ be a point on segment $AC$ such that $AD$ is twice the length of $DC$. If the length of $AD$ is $a$ units and $BC$ is $b$ units, then find the length of segment $AB$.

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