
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 $ABC$, the angle $BAC$ is right, and the lengths of the sides $AB$ and $BC$ are 5 and 6 respectively. Point $K$ divides side $AC$ in the ratio 3:1, starting from point $A$. Let $AH$ be the altitude of triangle $ABC$. Which is greater: 2 or the ratio of the length of $BK$ to the length of $AH$?

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