
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 a right-angled triangle $ABC$ with $\angle C = 90^\circ$, the heights from $A$ and $B$ to side $BC$ and $AC$ respectively are $5$ and $15$. What is the smallest integer value for the third altitude from $C$ onto $AB$?

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