
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
Three frogs have learned to jump on a ladder. Each can jump both up and down, but only by certain numbers of rungs. The frogs start on the ground, and each wants to reach its favorite rung:

- The small frog can jump by 2 or 3 rungs and wants to reach the seventh rung.
- The medium frog can jump by 2 or 4 rungs and wants to reach the first rung.
- The large frog can jump by 6 or 9 rungs and wants to reach the third rung.

For each frog, decide whether their wish is achievable. If so, describe how. If not, explain why.

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