
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 sides of a triangle are $a=21 \mathrm{~cm}, b=20 \mathrm{~cm}, c=17 \mathrm{~cm}$. The angles opposite these sides are $\alpha$, $\beta$, and $\gamma$, respectively. The area of this triangle is $t$. On a sphere with a radius of $10 \mathrm{~cm}$, there is a spherical triangle with an area $t_{1}$ and angles $\alpha_{1}$, $\beta_{1}$, and $\gamma_{1}$. What is $\gamma_{1}$ if $t_{1}=t$, $\alpha_{1}=\alpha$, and $\beta_{1}=\beta$?

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