
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
If the function $f(x) = A\sin(\omega x + \varphi)$ ($A > 0$, $\omega > 0$, $0 \leq \varphi < \pi$) satisfies the following conditions:
(1) The graph of $f(x)$ coincides with its original graph for the first time when it is shifted to the left by $\pi$ units;
(2) For any $x \in \mathbb{R}$, $f(x) \leq f\left( \frac{\pi}{6} \right) = 2$ holds.
Then:
(I) Find the expression of $f(x)$;
(II) If the acute angle $\triangle ABC$ has an internal angle $B$ satisfying $f(B) = 1$, and the side opposite to $\angle B$, denoted as $b = 1$, find the range of the perimeter $l$ of $\triangle ABC$.

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