
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
Solve the following:<br/>$(1)$ Calculate: $\sqrt{25}+|1-\sqrt{3}|+\sqrt{27}$;<br/>$(2)$ Given $\frac{a}{4}=\frac{b}{5}=\frac{c}{7}$, and $a+b+c=48$, find the lengths of the sides $a$, $b$, and $c$ of triangle $ABC$.

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