
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
From point $A$, a road branches off to the right at an angle of $\alpha = 38^{\circ} 23^{\prime}$ and leads straight to bridge $C$. From point $B$ on the main road, located $5.3 \mathrm{~km}$ further, another road branches off to the right and, after traveling $6 \mathrm{~km}$ straight, also leads to bridge $C$. From point $B$, a straight road branches off to the left at an angle of $\beta = 48^{\circ} 21.5^{\prime}$ and, after traveling $7 \mathrm{~km}$, reaches bridge $D$. The same river flows under both bridges, forming a circular arc with a radius of $9 \mathrm{~km}$ between $C$ and $D$. A battalion departs from point $A$ at 3:55 AM heading straight to bridge $C$ at a speed of $6 \mathrm{~km/h}$, to continue their journey by water, traveling at $10 \mathrm{~km/h}$ to bridge $D$.

When should the company leave from point $A$, traveling via point $B$ at a speed of $5 \mathrm{~km/h}$, to reach bridge $D$ at the same time as the battalion?

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