
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
In triangle $\triangle ABC$, $|AB|=1$, $|AC|=\sqrt{3}$. If $|\overrightarrow{AB} + \overrightarrow{AC}| = |\overrightarrow{BC}|$, then the shape of $\triangle ABC$ is _______ ; if there exists a $\lambda \in \mathbb{R}$ such that $|\lambda \overrightarrow{AB} - \overrightarrow{AC}| \leq \sqrt{2}$ is valid, then the range of $\overrightarrow{AB} \cdot \overrightarrow{AC}$ is _______ 
(① Acute triangle ② Obtuse triangle ③ Right triangle, fill in the serial number on the line).

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