
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
Let \(\mathbf{a}, \mathbf{b},\) and \(\mathbf{c}\) be vectors such that \(\|\mathbf{a}\| = 5,\) \(\|\mathbf{b}\| = 3,\) and \(\|\mathbf{c}\| = 4\) and 
\[
\mathbf{a} + \mathbf{b} + \mathbf{c} = \mathbf{k},
\]
where \(\mathbf{k}\) is a known vector with \(\|\mathbf{k}\| = 2.\) Compute \(\mathbf{a} \cdot \mathbf{b} + \mathbf{a} \cdot \mathbf{c} + \mathbf{b} \cdot \mathbf{c}.\)

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