
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 $\triangle \mathrm{ABC}$, $\mathrm{AB} = 13$ cm, $\mathrm{AC} = 10$ cm, and $\mathrm{AH} \perp \mathrm{BC}$. Point $D$ is located between $\mathrm{H}$ and $\mathrm{C}$ such that $\angle BAD = 60^{\circ}$ and $\angle DAC = 2 \angle HAD$. Find the ratio $\mathrm{BH}:\mathrm{HC}$.

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