
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 triangle $\Delta ABC$ with corresponding sides $a$, $b$, and $c$ for internal angles $A$, $B$, and $C$, where $A=60^{\circ}$, $b=1$, and $c=4$, find the value of $a$ and the expression $\frac{a+b+c}{\sin A+\sin B+\sin C}$.

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