
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 $\triangle XYZ$, where $X < Y$, an altitude is drawn from $Z$ to side $XY$, splitting angle $Z$ into $Z_1$ adjacent to side $y$ (opposite $X$) and $Z_2$ adjacent to side $x$ (opposite $Y$). Additionally, the angle of elevation of $Y$ as seen from $X$ across $XY$ is $10^\circ$. Determine the relationship between $Z_1$ and $Z_2$ given $Y = 50^\circ$ and $X = 40^\circ$.
A) \( Z_1 + Z_2 = 100^\circ \)
B) \( Z_1 - Z_2 = 10^\circ \)
C) \( Z_1 + Z_2 = 90^\circ \)
D) \( Z_1 - Z_2 = 30^\circ \)

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