
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
Given that the line $l$ makes an angle of $45^{\circ}$ with the plane $\alpha$, and the line $m$ is contained in $\alpha$. If the projection of $l$ onto $\alpha$ also makes an angle of $45^{\circ}$ with the line $m$, find the angle between the lines $l$ and $m$.

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