
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 the value of $\tan 3.75^\circ$ which can be expressed in the form:
\[
\tan 3.75^\circ = \sqrt{a} - \sqrt{b} + \sqrt{c} - d
\]
where \( a, b, c, d \) are positive integers with \( a \geq b \geq c \geq d \). Calculate \( a + b + c + d \).

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