
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
A right triangle $\triangle ABC$ has $\angle BAC=90^\circ$. If $\angle BCA = \theta$, point D is on $\overline{AC}$, and $\overline{BD}$ bisects $\angle ABC$, express $AD$ in terms of $s$ and $c$, where $s = \sin \theta$ and $c = \cos \theta.$

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