
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
The height of a tower \( C C_{1} \) looks from the endpoints of a horizontal distance \( A B=c \) at the same level as the base point \( C \) under elevation angles \(\delta=12^{\circ} 05^{\prime}\) and \(\varepsilon=6^{\circ} 55^{\prime}\), respectively. What is the height of \( C C_{1} \) if \( c=333.4 \ \mathrm{m} \) and \(\angle B A C =\alpha=103^{\circ} 21^{\prime}\)?

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