
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
There are linear transformations \(A x = \{x_2 - x_3, x_1, x_1 + x_3\}\) and \(B x = \{x_2, 2 x_2, x_1\}\) for the vector \(x = \{x_1, x_2, x_3\}\). Find the mapping \(B \cdot (2A - B)x\).

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