
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 solid $\text{NH}_{4}\text{I}$ is placed in a closed container and undergoes the following reactions at a certain temperature: $\text{①NH}_{4}\text{I(s)⇌ NH}_{3}\text{(g)+HI(g)}$, $\text{②2HI(g)⇌ H}_{2}\text{(g)+I}_{2}\text{(g)}$. At equilibrium, $\text{c(H}_{2}\text{)=0.5 mol·L}^{-1}$, $\text{c(HI)=4 mol·L}^{-1}$. Calculate the equilibrium constant for reaction $\text{①}$ and reaction $\text{②}$, and the equilibrium constant for the reaction $\text{H}_{2}\text{(g)+I}_{2}\text{(g)⇌ 2HI(g)}$ at the same temperature.

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