Chlorine is a halogen that undergoes a disproportionation reaction in cold, alkaline conditions.

When chlorine gas is reacted with cold, dilute sodium hydroxide solution, it forms sodium chloride solution, sodium chlorate(I) ($NaClO$), and water.

Complete the balanced equation for this reaction, including the three missing chemical formulae and their corresponding state symbols.

$$.....\; (.....)+2NaOH\; (aq)\to .....\; (.....)+NaClO\; (aq)+.....\; (.....)$$