
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 projectile is fired vertically upwards with an initial velocity of $c=99 \text{ m/sec}$. The explosion is heard 5 seconds after the moment of firing. At what height does the explosion occur, considering the speed of sound is $c=333 \text{ m/sec}$ and the acceleration due to gravity is $g=9.806 \text{ m/sec}^2$? (Accurate to 0.001 units; assume air resistance is negligible.)

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