
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
Given that in triangle $ABC$, $\angle BAC = 50^\circ$, $\angle CBA \leq 100^\circ$, $AB=1$, and $AC \geq BC$, find the value of $\angle CBA$ for which triangle $ABC$ maximizes the length of the altitude from $A$ to $BC$.

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