
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 $\overline{AD},$ $\overline{BE},$ $\overline{CF}$ be the altitudes of acute triangle $ABC.$  If
\[ 5 \overrightarrow{AD} + 3 \overrightarrow{BE} + 2 \overrightarrow{CF} = \mathbf{0},\] compute $\angle BAC,$ in degrees.

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