
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

The rules of a game are as follows: A player has four skills—water, fire, wind, and earth. Each skill requires a certain number of crystals to activate, and the specific effects are as follows:

- Water: Consumes 4 crystals and reduces the enemy's health by 4 points (if the enemy’s health is less than 4 points, they are killed directly).
- Fire: Consumes 10 crystals and reduces the enemy’s health by 11 points (if the enemy’s health is less than 11 points, they are killed directly).
- Wind: Consumes 10 crystals and reduces the enemy’s health by 5 points (if the enemy’s health is less than 5 points, they are killed directly) and the next skill’s crystal cost is halved (e.g., using the water skill after using the wind skill will cost only 2 crystals).
- Earth: Consumes 18 crystals and halves the enemy's health (if the enemy’s health is an odd number, 1 is added before halving).

If the enemy’s health is 120 points, how many crystals are needed at least to kill the enemy (reducing their health to 0)?

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