
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
(For the experimental class)  
(1) Solve the inequality: $x + |2x - 1| < 3$;  
(2) Let $x, y, z \in \mathbb{R}$, and satisfy: $x^2 + y^2 + z^2 = 1$, $x + 2y + 3z = \sqrt{14}$, find the value of $x + y + z$.

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