
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
A material point moves linearly inside a $60^{\circ}$ angle. Having exited from the vertex of this angle, the point after some time is at a distance $a$ from one side of the angle and at a distance $b$ from the other side. Then it changes its direction and simply falls the shortest distance to the side it was closer to. Find the length of the path traveled by the point, given that $a < b$.

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