
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 \( m \) be a real number, and vectors \(\boldsymbol{a} = \left(1 + 2^{m}, 1 - 2^{m}\right)\) and \(\boldsymbol{b} = \left(4^{m} - 3, 4^{m} + 5 \right)\). The minimum value of the dot product \(\boldsymbol{a} \cdot \boldsymbol{b}\) is ______.

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