
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
Determine vector \(\mathbf{b}\) given that vectors \(\mathbf{a}\) and \(\mathbf{b}\) satisfy:
\[\mathbf{a} + \mathbf{b} = \begin{pmatrix} 8 \\ -1 \\ -4 \end{pmatrix},\]
where \(\mathbf{a}\) is parallel to \(\begin{pmatrix} 2 \\ 2 \\ 2 \end{pmatrix},\) and \(\mathbf{b}\) is orthogonal to \(\begin{pmatrix} 2 \\ 2 \\ 2 \end{pmatrix}.\)

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