
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 **a**, **b**, and **c** are vectors such that **||a|| = ||b|| = 2**, **||a + b|| = 2\sqrt{2}**, and
\[
**c - 2a - 3b = 4 (a \times b)**,
\]
find **a · c**.

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