
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
(1) Calculate: $4\sin60^\circ-|-1|+(\sqrt{3}-1)^0+\sqrt{48}$;
(2) Solve the system of inequalities: $\begin{cases} \frac{1}{2}(x-1)\leq1 \\ 1-x<2\end{cases}$, and write out the largest integer solution of this system of inequalities.

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