
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 \( x, y \) and \( z \) are positive real numbers such that \(\frac{x+y-z}{z}=\frac{x-y+z}{y}=\frac{-x+y+z}{x}\) and \( a=\frac{(x+y) \cdot(y+z) \cdot(z+x)}{x y z} \), find the value of \( a \).

Let \( u \) and \( t \) be positive integers such that \( u+t+u t=4 a+2 \). If \( b=u+t \), find the value of \( b \).

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